The Basic Principles of Electricity

Electricity

Electricity, simply put, is the flow of electric current along a conductor. This electric current takes the form of free electrons that transfer from one atom to the next. Thus, the more free electrons a material has, the better it conducts. There are three primary electrical parameters: the volt, the ampere and the ohm.1. The Volt

The pressure that is put on free electrons that causes them to flow is known as electromotive force (EMF). The volt is the unit of pressure, i.e., the volt is the amount of electromotive force required to push a current of one ampere through a conductor with a resistance of one ohm.

2. The Ampere

The ampere defines the flow rate of electric current. For instance, when one coulomb (or 6 x 1018 electrons) flows past a given point on a conductor in one second, it is defined as a current of one ampere.

3. The Ohm

The ohm is the unit of resistance in a conductor. Three things determine the amount of resistance in a conductor: its size, its material, e.g., copper or aluminum, and its temperature. A conductor’s resistance increases as its length increases or diameter decreases. The more conductive the materials used, the lower the conductor resistance becomes. Conversely, a rise in temperature will generally increase resistance in a conductor.

 

Ohm’s Law

Ohm’s Law defines the correlation between electric current (I), voltage (V), and resistance (R) in a conductor.

Ohm’s Law can be expressed as: V = I × R

Where: V = volts, I = amps, R = ohms

 

Ampacity

Ampacity is the amount of current a conductor can handle before its temperature exceeds accepted limits. These limits are given in the National Electrical Code (NEC), the Canadian Electrical Code and in other engineering documents such as those published by the Insulated Cable Engineers Association (ICEA). It is important to know that many external factors affect the ampacity of an electrical conductor and these factors should be taken into consideration before selecting the conductor size.

ELECTRICS DEPARTMENT

Basic electricity:

Electricity is the flow of electrons from one place to another. Electrons can flow through any material, but does so more easily in some than in others. How easily it flows is called resistance. The resistance of a material is measured in Ohms.

Matter can be broken down into:

Conductors: electrons flow easily. Low resistance. Semi-conductors: electron can be made to flow under certain circumstances. Variable resistance

according to formulation and circuit conditions. Insulator: electrons flow with great difficulty. High resistance.

Since electrons are very small, as a practical matter they are usually measured in very large numbers. A Coulomb is 6.24 x 1018 electrons. However, electricians are mostly interested in electrons in motion. The flow of electrons is called current, and is measured in AMPS. One amp is equal to a flow of one coulomb per second through a wire.

Making electrons flow through a resistance requires an attractive force to pull them. This force, called Electro-Motive Force or EMF, is measured in volts. A Volt is the force required to push 1 Amp through 1 Ohm of resistance.

As electrons flow through a resistance, it performs a certain amount of work. It may be in the form of heat or a magnetic field or motion, but it does something. This work is called Power, and is measured in Watts. One Watt is equal to the work performed by 1 Amp pushed by 1 Volt through a resistance.

NOTE:

AMPS is amount of electricity.VOLTS is the Push, not the amount.

OHMS slows the flow.WATTS is how much gets done.

There are 2 standard formulae that describe these relationships.

Ohm's Law: Where

R = Resistance (ohms)

E = Electro-motive Force (volts)

<>I = Intensity of Current (amps) R = E / I

To express work done: Power formula (PIE Law):

Where:

P = Power (watts)

I = Intensity of Current (amps)

E = Electro-motive Force (volts)

P = IE

This law is often restated in the units of measure as the West Virginia Law:

W = VAforWatts = Volts x Amps

All this is important because all electrical equipment has a limit to how much electricity it can handle safely, and you must keep track of load and capacities to prevent failure, damage, or a fire.

For example, a lamp is rated at 1000 w. @ 120 v. That means that at 120 volts it will use:

1000 w. / 120 v. = 8.33 a.

A common shortcut is to use 100 v. instead of 120. This makes calculating easier and builds in some headspace. So:

1000 w./ 100 v. = approx. 10 a.

A Simple Circuit:

The simplest circuit has a power source, like a battery or outlet, a wire running from the "hot" side to a "load", then a wire from the load back to the power source. There is also usually a switch to "open" or "close" the circuit. The load will function only when the circuit is closed or complete.

In more complex circuits where more than one load is connected, they may be either in series or in parallel. In a series circuit, current must pass trough one to get to the next. Voltage is divided between them. If one goes out, they all go out.

In a parallel circuit, each load is electrically connected to the source at the same point, each gets the full voltage simultaneously. If one goes out, the rest stay lit.

Most circuits are combinations of the two types. Circuit breakers and fuses are in series with the load, but multiple loads on a circuit are paralleled.

Circuit breakers and fuses can be placed in the supply circuit before the plug, as in lighting circuits, or between the plug and the load internally, as in most sound equipment, or both.

Cable, connectors, and circuits are all rated in amps according to size.

Cable

There are many types of cable, but the electrical code allows only certain types to be used. Stage use is very hard on equipment. Cable may be walked on, runover by scenery or vehicles, pulled and dragged, and pinched. The emphasis is therefore on flexibility and durability.

For single circuit used, ONLY type S or SO cables are permitted. Type S is a heavy-duty rubber covered cable. Type SO is a heavy duty Neoprene (synthetic rubber, oil resistant) covered cable. It must be a three wire cable, with black, white and green conductors. Type SJ, with a lighter weight rubber covering, is specifically NOT permitted. For single conductor feeder cable use, welding cable was once common is specifically NOT permitted. It must be Types SC, SCE, PPE or similar Entertainment and Stage Cable, which has an extra-heavy duty cover and very flexible wire inside.

Wire gauge    Ampacity

#18 7 a.

#16 10 a.

#14 15 a.

#12 20 a.

#10 25 a.

#00 (2/0) 300 a.

#0000 (4/0) 405 a.

These are approximate values for the cables typically used in theatre. Other types and methods may be rated differently.

Connectors

Connectors allow temporary connections to be made and broken quickly and safely. Male connectors have exposed contacts. Female connectors have internal contacts inside an insulating shell with holes for plugging the two together. Think biology.

The male is always on the load side of a connection, the female on the line side; "the female has the power!"

parallel Blade (Edison): the standard household plug, this is found on much equipment but is not durable enough for stage lights. The standard configuration, two parallel blades and a U-ground, is rated at 15 a. only. Usually the"hot" terminal is copper colored and the "neutral" is silver colored, and the "ground" is green.

Stage Pin (a.k.a. NEMA designation, 5T-20): has round 1/4" pins, and is very durable. Most common dedicated stage connector. Rated at 20 a. The center pin is "ground", the outside pin nearest the ground is the "neutral", and the other is the "hot".

3-pin Twist Lock (a.k.a. NEMA L5-20): has three curved blades which are locked into the receptacle by rotating it 1/8 turn after insertion. Rated at 20 a. One blade has a tab bent towards center; that is the ground. The slightly larger blade with silver screw is "neutral", and the small blade with the copper screw is "hot".

Cam-locks: single wire connector for large wire, 2/0 or 4/0. Locked in place by rotating 1/2 turn after insertion. Comes in colors to indicate which leg is which. Rated at over 400 a. In most common size on stage. Also available in a mini-cam size for #1 cable, rated at 100 a.

Cable Accessories:

Two-fers: Y-cord with one male and two female connectors, for plugging two devices into one outlet.

Three-fers: same thing, 3 females.

Adaptors: a male connector on one end and a female of a different type on the other. Used to plug a device into a different type of outlet.

POWER DISTRIBUTION

There are broadly two form in which electricity can be generated, Direct Current and Alternating current. Direct Current is the type of electricity supplied by a battery. One terminal is positively charged, the other negatively charged, and electricity flows from one to the other, always in the same direction. However, while it is simple to make and control, DC does not travel well over long distances; it gets used up by the resistance in the transmission lines, and is gone before it gets to where it is needed.

Alternating Current also has a positive and a negative terminal, but the polarity and the direction of flow alternates many times per second. In the United States, electricity alternates polarity 120 times per second, or 60 full cycles per second, i.e. 60 Hz. AC can travel well over long distances, and so it the choice for power distribution lines.

There is no difference between amps or volts between AC or DC. Some devices can ONLY operate on one type of system or the other, but otherwise a volt is a volt.

Road shows and concert tours typically bring in their own lighting and sound rigs, which means their dimmer racks and sound distribution boxes must be tied in to a power source able to supply large amounts of current.

Power is usually generated at a distance from where it is used. It is supplied as 3-phase power at very high voltages.This allows many kilowatts to flow through fairly small conductors because amperage is effectively small. There are 3 hots, each 120 degrees out-of-phase with the next when their sine waves are plotted against each other, hence the term "3 phase". There is no neutral. This configuration is called Delta, and is the same type (at much lower voltages) use to run 3-phase motors.

The power level is brought down through a series of substations. At each step transformers reduce the voltage and increase the amperage until it reaches the line transformers outside the building. At that point, the Delta service is converted to a Wye service, and is brought into the building at the "service entrance".

The Wye service has the same three hot legs, plus an electrical neutral created at the transformer. By this time in either Wye or Delta, the line voltage has been brought down to where each hot terminal is 120 volts above earth potential, called "ground", and in the case of a Wye service, each hot is also 120 v. above the Neutral as well. However, due to the geometry of the hot phases, there is a difference of 208 v. (not 240 v.) between any two hots in either type of 3-phase system.

This is different from the Single-phase system found in some older theatres, and commonly in private homes.

In this service two hots are drawn from each end of one phase of a Delta (hence Single phase), and a neutral created at the transformer. These are brought into the building at the service entrance. Between either hot and the neutral there is 120 v., just as in the Wye system. However, there is 240 v., not 208 v, between the two hots. Single phase is rarely found in industry, including theatre, because it is not as efficient for supplying the large amounts of power needed.

At the service entrance the Neutral of the Wye (or of a single phase) system must be bonded to a grounding system buried in the earth outside. It is VERY important that the ground and neutral NOT be connected at any other point, or an unsafe situation could be created.

Tying in Power

When in comes to permanent commercial wiring, the Electrical Code requires that only licensed electricians do the work. However, the Code has an exemption for the Entertainment industry. "Qualified Personnel" are allowed to make TEMPORARY hookups to an electrical service. That means that a qualified stagehand can tie a portable dimmer rack to a distribution box, but cannot run permanent wires to that box OR install a PERMANENT dimmer rack. The key phrase is "Qualified personnel". Only stagehands have who been trained to do so are allowed to make hookups. The Code also grants another exemption to theatre not found in other industries. Theatre is allowed to use single conductors and connectors (that is feeder cable with Camlock connectors). But as it is VITAL that the connections be made in the proper order, only trained and qualified personnel are permitted to make those connections.

The distribution box where temporary equipment is tied in to the electrical supply is called a Company Switch, a Distro, or a "Bull switch".

Inside the distro are lugs for connecting the wires. There are three lugs for connecting the "hot" wires, each of which is connected to a fuse or a circuit breaker. They are typically referred to as Leg A, B, and C; or leg X, Y, and Z. They may be black or marked with any color EXCEPT White, light grey, or green. There is also a lug for the Neutral, which does NOT have a fuse or breaker, which MUST be marked white or light grey, and a lug for the Ground wire, which is usually bolted directly to the metal distro box. (According to Code, the box and its conduit are suppose to be grounded, but if they are not, a separate grounding wire, marked with green, must be run to the box.) There will also be an access hole through which the temporary wires are passed. The hole should have a bushing to prevent the box from cutting through the insulation of the wire.

The proper procedure MUST be followed when connecting the cables, or an unsafe situation can occur. DO NOT TAKE SHORTCUTS!

Lay out the feeder tails so they are ready to be connected. NOTE: Code requires the use tails which can be disconnected within 10 feet of the distro box). The tails should NOT be connected to the feeder cables yet.

Turn off the bull switch if it is not already off (the box will not open if the switch is on unless the box is broken). Open the box and MAKE SURE the "hot" terminals are really "dead" using a meter or tester.

Insert the Green tail wire and fasten securely to the ground lug. Insert the White white and fasten to the Neutral lug.

Insert the Hot tails one at a time and attach them securely to the three "hot" terminals, the ones attached to the fuses or breakers. These wires are usually marked with Black, Red, and Blue. It does not really matter at this point which wire is connected to which hot terminal, but the convention is usually in the order: Black, Red, Blue.

Close the box and make sure the connectors on the tails are clear. Turn on the Bull switch. Test each wire with a meter by carefully inserting the leads from the meter into the open feeder

connectors. You should get:o Between Neutral and Ground: 0 volts.o Between each Hot wire and Neutral: 120 v.o Between each Hot wire and the Ground: 120 v.o Between each Hot and any other Hot: 208 v.

If you get ANY OTHER READINGS, check your wiring again!

If everything checks OK, turn off the Bull switch and inform the road electrician.

When the feeder cables are connected to the dimmer rack or sound distro, and when the feeders are connected to the tails, CONNECT THEM IN THE SAME ORDER!, That is: first Green, then White, then the three Hots. Connect them with the power turned off but always treat them as though the power is on anyway. Someday it may be!

Also, NEVER PLUG THE HOTS IN FIRST! The equipment may try to close a circuit through two hots and put 208 v. through a circuit meant for 120 v., and destroy the equipment, or worse yet electrocute someone!

Many rigging motors are three-phase motor, using three hots and NO neutral. Occasionally a motor may run backwards. In that case, simply swap any two hots and the motor will run the other way.

Basic Electrical Concepts & Terms

Basic electrical concepts and terms - current, voltage, resistance, power, charge, efficiency.

Electrical voltage Electrical current Electrical resistance Electric power Electric charge Power efficiency Power factor

Electrical Voltage

Electrical voltage is defined as electric potential difference between two points of an electric field.

Using water pipe analogy, we can visualize the voltage as height difference that makes the water flow down.

V = φ2 - φ1

V is the voltage between point 2 and 1 in volts (V).

φ2 is the electric potential at point #2 in volts (V).

φ1 is the electric potential at point #1 in volts (V).

 

In an electrical circuit, the electrical voltage V in volts (V) is equal to the energy consumption E in joules (J)

divided by the electric charge Q in coulombs (C).

V is the voltage measured in volts (V)

E is the energy measured in joules (J)

Q is the electric charge measured in coulombs (C)

Voltage in series

The total voltage of several voltage sources or voltage drops in series is their sum.

VT = V1 + V2 + V3 +...

VT - the equivalent voltage source or voltage drop in volts (V).

V1 - voltage source or voltage drop in volts (V).

V2 - voltage source or voltage drop in volts (V).

V3 - voltage source or voltage drop in volts (V).

Voltage in parallel

Voltage sources or voltage drops in parallel have equal voltage.

VT = V1 = V2 = V3 =...

VT - the equivalent voltage source or voltage drop in volts (V).

V1 - voltage source or voltage drop in volts (V).

V2 - voltage source or voltage drop in volts (V).

V3 - voltage source or voltage drop in volts (V).

Voltage divider

For electrical circuit with resistors (or other impedance) in series, the voltage drop Vi on resistor Ri is:

Kirchhoff's voltage law (KVL)

The sum of voltage drops at a current loop is zero.

∑ Vk = 0

DC circuit

Direct current (DC) is generated by a constant voltage source like a battery or DC voltage source.

The voltage drop on a resistor can be calculated from the resistor's resistance and the resistor's current, using Ohm's law:

Voltage calculation with Ohm's law

VR = IR × R

VR - voltage drop on the resistor measured in volts (V)

IR - current flow through the resistor measured in amperes (A)

R - resistance of the resistor measured in ohms (Ω)

AC circuit

Alternating current is generated by a sinusoidal voltage source.

Ohm's law

VZ = IZ × Z

VZ - voltage drop on the load measured in volts (V)

IZ - current flow through the load measured in amperes (A)

Z - impedance of the load measured in ohms (Ω)

Momentary voltage

v(t) = Vmax × sin(ωt+θ)

v(t) - voltage at time t, measured in volts (V).

Vmax - maximal voltage (=amplitude of sine), measured in volts (V).

ω      - angular frequency measured in radians per second (rad/s).

t        - time, measured in seconds (s).

θ       - phase of sine wave in radians (rad).

RMS (effective) voltage

Vrms = Veff  =  Vmax / √2 ≈ 0.707 Vmax

Vrms -  RMS voltage, measured in volts (V).

Vmax - maximal voltage (=amplitude of sine), measured in volts (V).

Peak-to-peak voltage

Vp-p = 2Vmax

Voltage drop

Voltage drop is the drop of electrical potential or potential difference on the load in an electrical circuit.

Voltage Measurement

Electrical voltage is measured with Voltmeter. The Voltmeter is connected in parallel to the measured component or circuit.

The voltmeter has very high resistance, so it almost does not affect the measured circuit.

Voltage by Country

AC voltage supply may vary for each country.

European countries use 230V while north America countries use 120V.

 

Country Voltage

[Volts]

Frequency

[Hertz]Australia 230V 50HzBrazil 110V 60HzCanada 120V 60HzChina 220V 50HzFrance 230V 50HzGermany 230V 50HzIndia 230V 50HzIreland 230V 50HzIsrael 230V 50Hz

Italy 230V 50HzJapan 100V 50/60HzNew Zealand

230V 50Hz

Philippines 220V 60HzRussia 220V 50HzSouth Africa 220V 50HzThailand 220V 50HzUK 230V 50HzUSA 120V 60Hz

Electric current definition

Electrical current is the flow rate of electric charge in electric field, usually in electrical circuit.

Using water pipe analogy, we can visualize the electrical current as water current that flows in a pipe.

The electrical current is measured in ampere (amp) unit.

Electric current calculation

Electrical current is measured by the rate of electric charge flow in an electrical circuit:

i(t) = dQ(t) / dt

The momentary current is given by the derivative of the electric charge by time.

i(t) is the momentary current I at time t in amps (A).

Q(t) is the momentary electric charge in coulombs (C).

t is the time in seconds (s).

 

When the current is constant:

I = ΔQ / Δt

I is the current in amps (A).

ΔQ is the electric charge in coulombs (C), that flows at time duration of Δt.

Δt is the time duration in seconds (s).

 

Example

When 5 coulombs flow through a resistor for duration of 10 seconds,

the current will be calculated by:

I = ΔQ / Δt  = 5C / 10s = 0.5A

Current calculation with Ohm's law

The current IR in anps (A) is equal to the resistor's voltage VR in volts (V) divided by the resistance R in ohms (Ω).

IR = VR / R

Current direction

current type from to

Positive charges + -

Negative charges - +

Conventional direction + -

Current in series circuits

Current that flows through resistors in series is equal in all resistors - just like water flow through a single pipe.

ITotal = I1 = I2 = I3 =...

ITotal - the equivalent current in amps (A).

I1 - current of load #1 in amps (A).

I2 - current of load #2 in amps (A).

I3 - current of load #3 in amps (A).

Current in parallel circuits

Current that flows through loads in parallel - just like water flow through parallel pipes.

The total current ITotal is the sum of the parallel currents of each load:

ITotal = I1 + I2 + I3 +...

ITotal - the equivalent current in amps (A).

I1 - current of load #1 in amps (A).

I2 - current of load #2 in amps (A).

I3 - current of load #3 in amps (A).

Current divider

The current division of resistors in parallel is

RT = 1 / (1/R2 + 1/R3)

or

I1 = IT × RT / (R1+RT)

Kirchhoff's current law (KCL)

The junction of several electrical components is called a node.

The algebraic sum of currents entering a node is zero.

∑ Ik = 0

Alternating Current (AC)

Alternating current is generated by a sinusoidal voltage source.

Ohm's law

IZ = VZ / Z

IZ  - current flow through the load measured in amperes (A)

VZ - voltage drop on the load measured in volts (V)

Z  - impedance of the load measured in ohms (Ω)

Angular frequency

ω = 2π f

ω - angular velocity measured in radians per second (rad/s)

f  - frequency measured in hertz (Hz).

Momentary current

i(t) = Ipeak sin(ωt+θ)

i(t)      - momentary current at time t, measured in amps (A).

Ipeak - maximal current (=amplitude of sine), measured in amps (A).

ω      - angular frequency measured in radians per second (rad/s).

t        - time, measured in seconds (s).

θ       - phase of sine wave in radians (rad).

RMS (effective) current

Irms =  Ieff =  Ipeak / √2 ≈ 0.707 Ipeak

Peak-to-peak current

Ip-p = 2Ipeak

Current measurement

Current measurement is done by connecting the ammeter in series to the measured object, so all the measured current will flow through the ammeter.

The ammeter has very low resistance, so it almost does not affect the measured circuit.

Resistance definition

Resistance is an electrical quantity that measures how the device or material reduces the electric current flow through it.

The resistance is measured in units of ohms (Ω).

If we make an analogy to water flow in pipes, the resistance is bigger when the pipe is thinner, so the water flow is decreased.

Resistance calculation

The resistance of a conductor is resistivity of the conductor's material times the conductor's length divided by the conductor's cross sectional area.

R is the resistance in ohms (Ω).

ρ is the resistivity in ohms-meter (Ω×m)

l is the length of the conductor in meter (m)

A is the cross sectional area of the conductor in square meters (m2)

 

It is easy to understand this formula with water pipes analogy:

when the pipe is longer, the length is bigger and the resistance will increase. when the pipe is wider, the cross sectional area is bigger and the resistance will decrease.

Resistance calculation with ohm's law

R is the resistance of the resistor in ohms (Ω).

V is the voltage drop on the resistor in volts (V).

I is the current of the resistor in amperes (A).

Temperature effects of resistance

The resistance of a resistor increases when temperature of the resistor increases.

R2 = R1 × ( 1 + α(T2 - T1) )

R2 is the resistance at temperature T2 in ohms (Ω).

R1 is the resistance at temperature T1 in ohms (Ω).

α is the temperature coefficient.

Resistance of resistors in series

The total equivalent resistance of resistors in series is the sum of the resistance values:

RTotal = R1+ R2+ R3+...

Resistance of resistors in parallel

The total equivalent resistance of resistors in parallel is given by:

Measuring electrical resistance

Electrical resistance is measured with ohmmeter instrument.

In order to measure the resistance of a resistor or a circuit, the circuit should have the power supply turned off.

The ohmmeter should be connected to the two ends of the circuit so the resistance can be read.

Superconductivity

Superconductivity is the drop of resistance to zero at very low temperatures near 0ºK.

Electric Power

Electric power is the rate of energy consumption in an electrical circuit.

The electric power is measured in units of watts.

Electric power definition

The electric power P is equal to the energy consumption E divided by the consumption time t:

P is the electric power in watt (W).

E is the energy consumption in joule (J).

t is the time in seconds (s).

Example

Find the electric power of an electrical circuit that consumes 120 joules for 20 seconds.

Solution:

E = 120J

t = 20s

P = E / t = 120J / 20s = 6W

Electric power calculation

P = V · I

or

P = I 2 · R

or

P = V 2 / R

P is the electric power in watt (W).

V is the voltage in volts (V).

I is the current in amps (A).

R is the resistance in ohms (Ω).

Power of AC circuits

The formulas are for single phase AC power.

For 3 phase AC power:

 When line to line voltage (VL-L) is used in the formula, multiply the single phase power by square root of 3 (√3=1.73).

When line to zero voltage (VL-0) is used in the formula, multiply the single phase power by 3.

Real power

Real or true power is the power that is used to do the work on the load.

P = Vrms Irms cos φ

 

P      is the real power in watts [W]

Vrms  is the rms voltage = Vpeak/√2 in Volts [V]

Irms   is the rms current = Ipeak/√2 in Amperes [A]

φ      is the impedance phase angle = phase difference between voltage and current.

 

Reactive power

Reactive power is the power that is wasted and not used to do work on the load.

Q = Vrms Irms sin φ

 

Q      is the reactive power in volt-ampere-reactive [VAR]

Vrms  is the rms voltage = Vpeak/√2 in Volts [V]

Irms   is the rms current = Ipeak/√2 in Amperes [A]

φ      is the impedance phase angle = phase difference between voltage and current.

 

Apparent power

The apparent power is the power that is supplied to the circuit.

S = Vrms Irms

 

S      is the apparent power in Volt-amper [VA]

Vrms  is the rms voltage = Vpeak/√2 in Volts [V]

Irms   is the rms current = Ipeak/√2 in Amperes [A]

 

Real / reactive / apparent powers relation

The real power P and reactive power Q give together the apparent power S:

P2 + Q2 = S2

 

P      is the real power in watts [W]

Q      is the reactive power in volt-ampere-reactive [VAR]

S      is the apparent power in Volt-amper [VA]

What is electric charge?

Electric charge generates electric field. The electric charge influence other electric charges with electric force and influenced by the other charges with the same force in the opposite direction.

There are 2 types of electric charge:

Positive charge (+)

Positive charge has more protons than electrons (Np>Ne).

Positive charge is denoted with plus (+) sign.

The positive charge attracts other negative charges and repels other positive charges.

The positive charge is attracted by other negative charges and repelled by other positive charges.

Negative charge (-)

Negative charge has more electrons than protons (Ne>Np).

Negative charge is denoted with minus (-) sign.

Negative charge attracts other positive charges and repels other negative charges.

The negative charge is attracted by other positive charges and repelled by other negative charges.

Electric force (F) direction according to charge type

q1/q2 charges

Force on q1

chargeForce on q2

charge 

- / - ←⊝ ⊝→ repletion

+ / + ←⊕ ⊕→ repletion

- / + ⊝→ ←⊕ attraction

+ / - ⊕→ ←⊝ attraction

Charge of elementary particles

Particle Charge (C) Charge (e)

Electron 1.602×10-19 C -e

Proton 1.602×10-19 C +e

Neutron 0 C 0

Coulomb unit

The electric charge is measured with the unit of Coulomb [C].

One coulomb has the charge of 6.242×1018 electrons:

1C = 6.242×1018 e

Electric charge calculation

When electric current flows for a specified time, we can calculate the charge:

Constant current

Q = I · t

Q is the electric charge, measured in coulombs [C].

I is the current, measured in amperes [A].

t is the time period, measured in seconds [s].

Momentary current

Q is the electric charge, measured in coulombs [C].

i(t) is the momentary current, measured in amperes [A].

t is the time period, measured in seconds [s].

Electric Power Efficiency

Power efficiency

Power efficiency is defined as the ratio of the output power divided by the input power:

η = 100% · Pout / Pin

η is the efficiency in percent (%).

Pin is the input power consumption in watts (W).

Pout is the output power or actual work in watts (W).

Example

Electric motor has input power consumption of 50 watts.

The motor was activated for 60 seconds and produced work of 2970 joules.

Find the efficiency of the motor.

Solution:

Pin = 50W

E = 2970J

t = 60s

Pout = E / t  = 2970J / 60s = 49.5W

η = 100% * Pout / Pin = 100 * 49.5W / 50W = 99%

Energy efficiency

Energy efficiency is defined as the ratio of the output energy divided by the input energy:

η = 100% · Eout / Ein

η is the efficiency in percent (%).

Ein is the input energy consumed in joule (J).

Eout is the output energy or actual work in joule (J).

Example

Light bulb has input power consumption of 50 watts.

The light bulb was activated for 60 seconds and produced heat of 2400 joules.

Find the efficiency of the light bulb.

Solution:

Pin = 50W

Eheat = 2400J

t = 60s

Ein = Pin * t = 50W * 60s = 3000J

Since the light bulb should produce light and not heat:

Eout = Ein - Eheat = 3000J - 2400J = 600J

η = 100 * Eout / Ein = 100% * 600J / 3000J = 20%

Power Factor

In AC circuits, the power factor is the ratio of the real power that is used to do work and the apparent power that is supplied to the circuit.

The power factor can get values in the range from 0 to 1.

When all the power is reactive power with no real power (usually inductive load) - the power factor is 0.

When all the power is real power with no reactive power (resistive load) - the power factor is 1.

Power factor definition

The power factor is equal to the real or true power P in watts (W) divided by the apparent power |S| in volt-ampere (VA):

PF = P(W) / |S(VA)|

PF - power factor.

P   - real power in watts (W).

|S|   - apparent power - the magnitude of the complex power in volt·amps (VA).

Power factor calculations

For sinusuidal current, the power factor PF is equal to the absolute value of the cosine of the apparent power phase angle φ (which is also is impedance phase angle):

PF = |cos φ|

PF is the power factor.

φ   is the apprent power phase angle.

 

The real power P in watts (W) is equal to the apparent power |S| in volt-ampere (VA) times the power factor PF:

P(W) = |S(VA)| × PF = |S(VA)| × |cos φ|

 

When the circuit has a resistive impedance load, the real power P is equal to the apparent power |S| and the power factor PF is equal to 1:

PF(resistive load) = P / |S| = 1

 

The reactive power Q in volt-amps reactive (VAR) is equal to the apparent power |S| in volt-ampere (VA) times the sine of the phase angle φ:

Q(VAR) = |S(VA)| × |sin φ|

Single phase circuit calculation from real power meter reading P in kilowatts (kW), voltage V in volts (V) and current I in amps (A):

PF = |cos φ| = 1000 × P(kW) / (V(V) × I(A))

 

Three phase circuit calculation from real power meter reading P in kilowatts (kW), line to line voltage VL-L in volts (V) and current I in amps (A):

PF = |cos φ| = 1000 × P(kW) / (√3 × VL-L(V) × I(A))

 

Three phase circuit calculation from real power meter reading P in kilowatts (kW), line to line neutral VL-N in volts (V) and current I in amps (A):

PF = |cos φ| = 1000 × P(kW) / (3 × VL-N(V) × I(A))

Power factor correction

Power factor correction is an adjustment of the electrical circuit in order to change the power factor near 1.

Power factor near 1 will reduce the reactive power in the circuit and most of the power in the circuit will be real power. This will also reduce power lines losses.

The power factor correction is usually done by adding capacitors to the load circuit, when the circuit has inductive components, like an electric motor.

Power factor correction calculation

The apparent power |S| in volt-amps (VA) is equal to the voltage V in volts (V) times the current I in amps (A):

|S(VA)| = V(V) × I(A)

The reactive power Q in volt-amps reactive (VAR) is equal to the square root of the square of the apparent power |S| in volt-ampere (VA) minus the square of the real power P in watts (W) (pythagorean theorem):

Q(VAR) = √(|S(VA)|2 - P(W)2)

The reactive power Q in volt-amps reactive (VAR) is equal to the square of voltage V in volts (V) divided by the reactance Xc:

Q(VAR) = V(V)2 / XC = V(V)

2 / (1 / (2πf(Hz)·C(F))) = 2πf(Hz)·C(F)·V(V)2

So the power factor correction capacitor in Farad (F) that should be added to the circuit in parallel is equal to the reactive power Q in volt-amps reactive (VAR) divided by 2π times the frequency f in Hertz (Hz) times the squared voltage V in volts (V):

C(F) = Q(VAR) / (2πf(Hz)·V(V)2)

Basic Electricity - Electrical Definition

Basic electricity is described in many ways. When an electric circuit flows through a conductor, a magnetic field (or "flux") develops around the conductor. The highest flux density occurs when the conductor is formed into a coil having many turns. In electronics and basic electricity, a coil is usually known as an inductor. If a steady DC current is run through the coil, you would have an electromagnet - a device with the properties of a conventional magnet, except you can turn it on or off by placing a switch in the circuit.

Basic Electrical TheoryThere are four basic electrical quantities that we need to know:

Current Potential Difference (Voltage) Power Resistance

Electrical CurrentCurrent is a flow of charge. Each electron carries a charge of 1.6 × 10-19 coulombs. This is far too small to be any use, so we consider electricity to flow in packets called coulombs. When there is a flow of 1 coulomb per second, a current of 1 amp is flowing. Current is measured in ampères, or amps (A).

Potential Difference Potential difference is often referred to as voltage. There are several ways of defining voltage; the correct physics definition is energy per unit charge, in other words, how big a job of work each lump of charge can do.

Power in a CircuitPower in a circuit can be worked out using the simple relationship:

Power (W) = Voltage (V) × Current (A)

Electrical ResistanceThis is the opposition to the flow of an electric current.

There's reciprocity in the interaction between electron flow and magnetism. If you sweep one pole of a magnet quickly past an electrical conductor (at a right angle to it), a voltage will be momentarily "induced" in the conductor. The polarity of the voltage will depend upon which pole of the magnet you're using, and in which direction it sweeps past the conductor.

This phenomenon becomes more apparent when the conductor is formed into a coil of many turns.

Figure 1 shows a coil mounted close to a magnet that is spinning on a shaft. As the north pole of the magnet sweeps past the coil, a voltage is induced in the coil, and, if there is a "complete" circuit, current will flow. As the south pole of the magnet sweeps past, a voltage of opposite polarity is induced, and current flows in the opposite direction.

This relationship in basic electricity is the fundamental operating principle of a generator. The output, known as alternating current, is the type of power that electric utility companies supply to businesses and homes. A practical generator would likely have two coils mounted on opposite sides of the spinning magnet and wired together in a series connection. Because the coils are in a series, the voltages combine, and the voltage output of the generator will be twice that of each coil.

Figure 2 is a graph of the voltage produced by such a generator as a function of time.

Let's assume that this happens to be a 120-volt, 60-Hz generator. The voltage at one point in the cycle momentarily passes through 0 volts, but it's headed for a maximum of 169.7 volts. After that point, the voltage declines, passing through 0 volts, then reverses its polarity, and has a negative "peak" of -169.7 volts.

This curve is known as a sine wave since the voltage at any point is proportional to the sine of the angle of rotation. The magnet is rotating 60 times a second, so the sine wave repeats at the same frequency, making the period of a single cycle one-sixtieth of a second.

Electricity appears in two forms: alternating current (AC) and direct current (DC). Direct current does not change directions-- the electron flow is always from the negative pole to the positive pole-- although as we mentioned before, the electrons themselves don't really "move," it's the holes that are created that "move." Direct current is almost always what is used inside of electronic devices to power the various internal components, but it is a harmful thing in audio signals, which are alternating current. Alternating current does change direction-- standard household electricity is alternating current, because of its flexibility in traveling long distances. It changes direction at a specific frequency-- 60 times per second, or 60 Hz (in the United States, Japan, and a couple of other countries; in Europe the standard is 50 Hz). Audio signals vary their direction-alternation according to the frequency in question.

AC - ALTERNATING CURRENTAlternating current or AC electricity is the type of electricity commonly used in homes and businesses throughout the world.

While the flow of electrons through a wire in direct current (DC) electricity is continuous in one direction, the current in AC electricity alternates in direction. The back-and-forth motion occurs between 50 and 60 times per second, depending on the electrical system of the country.

AC is created by an AC electric generator, which determines the frequency. What is special about AC electricity is that the voltage in can be readily changed, thus making it more suitable for long-distance transmission than DC electricity. But also, AC can employ capacitors and inductors in electronic circuitry, allowing for a wide range of applications.

DC - DIRECT CURRENTIn a direct-current system, it's easy to determine voltage because it is nonvarying or varies slowly over time. You can simply make a measurement with a DC voltmeter. But in an AC circuit, the voltage is constantly changing.

Electrical engineers state the voltage of an AC sine wave as the RMS (root-mean-square), a value equal to the peak value of the sine wave divided by the square root of two, which is approximately 1.414. If you know the RMS voltage, you can multiply it by the square

root of two to calculate the peak voltage of the curve. If you were to power a light bulb from 120V(RMS) AC, you would get the same amount of light from the bulb as you would by powering it from 120V DC. Yet another device uses electromagnetic induction: the transformer.

Just as an iron core improves the inductance of a coil, it has the same positive effect in a transformer, and most power transformers are wound on iron cores.

In order to understand how electricity is created and works it is necessary to look at how all matter is structured. All matter is made up of molecules that have a certain number of atoms, for example one molecule of water is made up of two atoms of hydrogen and one of oxygen giving a symbol of H 2 O. All other matter also has a symbol like this and is made up of atoms.

To be able to understand electricity however, the atom must be broken down even further into a nucleus, electrons and protons. The nucleus is made up of positively charged protons and neutrally charged neutrons that generally balance the number of negatively charged electrons, which are moving around the nucleus in a similar manner to the planets circling the sun.

The outer ring of electrons is called the Valency Shell and the electrons contained in this ring are called Valence Electrons. These are the electrons which are knocked or forced out to form a flow of electricity. If one or more electrons are moved out of the the atom it will leave the atom with more protons than electrons, which means that the atom will be positively charged.

One rule that is very prevalent in all forms of electricity, and also magnetism, is that like charges, or poles, repel and unlike charges, poles, will attract. This means that a positively charged object will attract a negatively charged one, but if both charges are the same then they will repel each other.