PEP Conceptual PhysicsClass Notes

Unit 5 – ElectricityChapter 13 – Electrical Systems

Section 13.1• Series Circuits

• Series Circuits

• Series Current

• Series Resistance

• Series Voltage

• Solving Series Problems

Series Circuits• Series Circuit – an electric circuit that has only one

path for the current• All the components are in a single path

• A flashlight in an example of a simple series circuit

• Holiday lights are another example• Look at Figure 13.1 on page 316

• Notice the backup (or shunt) wire

• It’s initially coated and acts as an insulator, so the bulb’s filament doesn’t short out

• If the filament fails, the coating melts and the shunt acts as a conductor to keep the current flowing

• This keeps the remaining bulbs burning

Series Current• Since there is only a single path for the current to

follow, all the devices in the path must have the same current• Current doesn’t just leak away to nowhere

• More on currents at a point when we get to parallel circuits in Section 13.2

• You can still use Ohm’s law for the circuit, but you must account for the multiple resistances

Series Resistance• To calculate the total resistance in a series circuit,

you add all the individual resistances together as shown on page 317

𝑅𝑡𝑜𝑡𝑎𝑙 = 𝑅1 + 𝑅2 + 𝑅3 +⋯

• The total resistance will always be larger than the largest individual resistor in the circuit

• Even wires have resistance, although it is usually negligible compared to other resistances in the circuit and can be ignored for most problems

Series Voltage• Voltage Gain – increase of electrical energy by an

electronic device as current passes through it

• Voltage Drop – decrease of electrical energy by an electronic device as current passes through it

• Sidebar on page 318 – Batteries and cells• What we normally call a battery is technically a cell – a

single chemical-to-electrical energy conversion unit

• A battery is really a series of individual cells

Series Voltage• Law of conservation of energy cannot be violated

• We studied that law back in Chapters 4 and 8

• Batteries and power sources result in voltage gains

• Resistors and devices result in voltage drops

• Kirchhoff’s Voltage Law – the sum of the voltage drops in a series circuit must equal the sum of the voltage gains to conserve energy• 𝑅 = 𝑅1 + 𝑅2 + 𝑅3 +⋯ Resistors in series

• 𝐼𝑅 = 𝐼𝑅1 + 𝐼𝑅2 + 𝐼𝑅3 +⋯ Multiply by constant 𝐼

• 𝑉 = 𝑉1 + 𝑉2 + 𝑉3 +⋯ Apply Ohm’s law

Solving Series Problems• Ohm’s law and Kirchhoff’s laws are especially useful

in series circuits• These can each be applied to solve parts of a problem

• Consider a typical problem• Compute the voltage gain for all batteries

• Compute the total resistance for all resistors

• Compute the current from voltage and resistance

• Compute voltage drop for each resistor

• Compute the voltage drop for all resistors and compare to the voltage gain – they should be equal!

Solving Series Problems• Series circuit of a battery and three bulbs

• The total voltage gain is the battery’s 12 V

• The total resistance is 1 Ω + 1 Ω + 1 Ω = 3 Ω

• The current is 12 V / 3 Ω = 4 A

• The voltage drop across each bulb is 1 Ω x 4 A = 4 V

• The total voltage drop is 4 V + 4 V + 4 V = 12 V

+ -

1 Ω 1 Ω 1 Ω

12 V

Section 13.2• Parallel Circuits

• Parallel Circuits

• Parallel Current

• Parallel Voltage

• Parallel Resistance

• Short Circuits

• Circuit Breakers and Fuses

Parallel Circuits• Parallel Circuit – an electric circuit with more than

one path or branch• Different paths contain different components

• Your home in an example of a parallel circuit• Each appliance or device is in its own circuit

• Advantages of parallel circuits• Each device receives the full amount of voltage

• Each device can be turned on or off independently

• A parallel circuit is like a line of customers at a bank waiting for a teller• People flow faster if more tellers are available

Parallel Current• Since there are multiple paths for the current to

follow, the devices in each path can have different currents• Each path can have different resistances

• The total current in a parallel circuit is the sum of the currents in each branch

• Kirchhoff’s Current Law – the total current entering a circuit branch must equal the current leaving the branch• Current doesn’t just leak away to nowhere

Parallel Voltage• Kirchhoff’s voltage law continues to apply for each

branch independently

“The voltage is the same for each branchof a parallel circuit” (page 322)

• Ohm’s law applies to each branch independently and to the circuit as a whole

Parallel Resistance• To calculate the total resistance in a parallel circuit,

add the reciprocals of all the individual resistances together and take the reciprocal of the result as shown on page 323

1

𝑅𝑡𝑜𝑡𝑎𝑙=

1

𝑅1+

1

𝑅2+

1

𝑅3+⋯

• The total resistance will always be less than the smallest individual resistor in the circuit

Solving Series Problems• Parallel circuit of a battery and two bulbs

• The total voltage gain is the battery’s 3 volts

• The total resistance is 1 / (1 / 1 Ω + 1 / 1 Ω) = 0.5 Ω

• The total current through battery is 3 V / 0.5 Ω = 6 A

• The current through each bulb is 3 V / 1 Ω = 3 A

• The total current through bulbs is 3 A + 3 A = 6 A

+ -

1 Ω

1 Ω

3 V

Short Circuits• Short Circuit – occurs when a circuit branch has a

very low resistance, creating a large current

• Consider a 0.01 Ω copper wire and 1.5 𝑉 battery

• 𝐼 =𝑉

𝑅=

1.5 𝑉

0.01 Ω= 1,500 𝐴

• When current flows through a wire, the resistance causes the wire to heat• This is the principle behind toasters, many stovetops,

and ovens

• If too much current flows in too small a wire, the wire overheats and may melt or start a fire

!!!

Circuit Breakers and Fuses• Most homes and well-made appliances or devices

are protected by circuit breakers or fuses

• Circuit Breaker – a device common to several branches (e.g., one room of a home) that will “trip” if the current exceeds the rated value• The rated value is usually 15 or 20 amps

• To reset the breaker, disconnect the offending appliance, reset the tripped breaker, and reconnect the appliances

• Fuse – like a circuit breaker, but once it has “blown”, it cannot be reset but must be replaced• Used in automobiles and some devices like computers

and multimeters

Section 13.3• Electrical Power, AC, and DC Electricity

• Electrical Power

• Paying for Electricity

• Direct (DC) Current

• Alternating (AC) Current

• Electricity, Power, and Heat

• Electricity in Homes and Building

Electrical Power• Electrical Power – the rate at which electrical

energy is changed into other forms of energy• The unit of electrical power is the watt (joule per second)

just like for mechanical power

• Its abbreviation is W

• Another common unit used by utility companies is the kilowatt (kW), or 1,000 watts

• Other common forms of energy are light, sound, and heat• A 100-W light bulb converts 100 joules of electrical

energy every second into light and heat

• Most appliances have a label indicating power usage

Electrical Power• The formula for computing electrical power is like

the formulas for Newton’s second law or Ohm’s law• And it can be written in three forms like the others

• 𝑃 is the power in watts (W)

• 𝐼 is the current in amps (A)

• 𝑉 is the voltage in volts (V)

𝐼 =𝑃

𝑉𝑉 =

𝑃

𝐼𝑃 = 𝐼𝑉

Paying for Electricity• Electric utility companies charge for the electrical

energy used during a month

• Energy equals power multiplied by time• 𝐸 = 𝑃𝑡

• The unit used on electric bills is a kilowatt-hour (kWh)

• The total electric bill is the energy used (in kWh) times the rate (in $ per kWh)• A 100-watt bulb operated for 100 hours uses 10 kWh

• At a rate of $0.15 per kWh, it costs $1.50 to operate

Direct (DC) Current• Direct Current (DC) – electric current that flows in

one direction only

• This is the type of current produced by a battery

• Some of the appliances or devices it operates are• Computers or cell phones

• Flashlights

• Most small hand-held devices (e.g., remotes)

• Some DC motors

Alternating (AC) Current• Alternating Current (AC) – electric current that

reverses its direction at regular intervals

• This is the type of electricity used by homes and businesses to operate appliances and machines• It is easier to generate because it is based upon circular

motion of a coil of wire in a magnetic field

• It is easier to transmit over long distances because its voltage can be “stepped up” (to tens of thousands of volts) to reduce losses and then “stepped down” (to 120 or 240 volts) for endpoint use

Alternating (AC) Current• In the United States, the standard for alternating

current is 120 volts at 60 cycles per second• The 120 volts is the “average” voltage

• The “peak” voltage is about 170 volts (+ and -)

• The 60 cycles per second means that the current reverses its direction 120 times each second• Positive to negative

• Negative to positive

• Other countries may use another voltage or cycle• Standard voltages are mostly either 120 or 240

• Standard cycles are mostly either 50 or 60

Comparing DC with AC

Electricity, Power, and Heat• To use more power, you must increase either the

voltage or the current• Some appliances, like stoves, refrigerators, and heat

pumps, use 240 volts instead of 120 volts

• Other appliances, like audio amplifiers and hair dryers, use more current at the standard 120 volts

• Using too much current can be dangerous• Too much current in a wire can cause it to overheat,

melt, or start fires

• Resistance is higher for longer and/or thinner wires

• To avoid overheating use wires as short as possible and as thick as possible

Electricity in Homes and Building• Circuit breakers are devices in a circuit box (in your

garage) that control the maximum current a branch (usually a room or special appliance) can use• If the current exceeds the rated value (usually 15 or 20

amps), then the breaker will “trip”

• The breaker can be reset when the “fault” is corrected

• Automobiles and sensitive instruments use a fuse instead of a breaker• The fuse will break or burn out and cannot be reset – it

must be replaced

Electricity in Homes and Building• Most home and office room outlets have three

holes to accommodate two- and three-pronged power cords• Some outlets are “polarized” with the neutral left slot

wider than the hot (120-volt) slot

Electricity in Homes and Building• Ground fault interrupters (GFI) circuits are used in

most kitchens, bathrooms and garages• If the circuit is shorted due to contact with water, the

loop to ground is detected and the GFI trips

• It can be reset by pressing the (usually) red button