Current, Resistance and Electromotive Force

Electric Current

Electric current I is the flow of charge Q through a cross-section A in a unit of time t.

QI

t

1C1 A

1 s

One ampere A is charge flowing at the rate of one coulomb per second.

A+

-Wire

+Q

t

Example 1. The electric current in a wire is 6 A. How much charge flows past a given point in a time of 3 s?

I = 6 A

; q

I q Itt

q = (6 A)(3 s) = 18 C

Exercise 1

1. What charge is delivered if:

a. a current of 10A flows for 25 seconds

b. a current of 250mA flows for 35 seconds

2. 4000 µC of charge flows past a point in 25 seconds. Calculate the current in the circuit.

Conventional Current

Electron flow: The direction of e- flowing from – to +.

Conventional current:The motion of +q from + to – has same effect.

We will be referring to conventional current in most of the circuits (even if electron flow may be the actual flow).

++

--

+ -

Electron flow

+ -+ -

e-

Conventional flow

+

RESISTANCE

• Any conductor has some resistance that it offers to the flow of current.

• Resistance is measured in Ohms (Ω)

Factors Affecting Resistance

1. The length L of the material. Longer materials have greater resistance.

1 W

L

2 W

2L

2. The cross-sectional area A of the material. Larger areas offer LESS resistance.

2 W

A

1 W

2A

Factors Affecting R (Cont.)

3. The temperature T of the material. The higher temperatures usually result in higher resistances.

4. The kind of material. Iron has more electrical resistance than a similar copper conductor.

Ro

R > Ro

Ri > RcCopper Iron

For semi-conductors, the higher the temperature, the lower the resistance.

Symbol of a resistor

Electromotive Force

A source of electromotive force (emf) is a device that uses chemical, mechanical or other energy to provide the potential difference necessary for electric current.

Power lines Battery Wind generatorPotential Difference (p.d.) is the energy in a cell used to push electrons round a circuit. It is measured in Volt (V). It is also known as voltage.

Water Analogy to EMF

Low

pressure

PumpWater

High

pressure

ValveWater

Flow

Constriction

Source of EMF

ResistorHigh

potential

Low

potential

Switch

E

RI

+ -

The source of emf (pump) provides the voltage(pressure) to force electrons (water) through electric resistance (narrow constriction).

Ohm’s Law

Ohm’s law states that the current I through a given conductor is directly proportional to the potential difference V between its end points.

Ohm’s law allows us to define resistance Rand to write the following forms of the law:

' :Ohm s law I V

; ; V V

I V IR RR I

Example 2. When a 3-V battery is connected to a light, a current of 6 mAis observed. What is the resistance of the light filament?

Source of EMF

RI

+ -

V = 3 V6 mA

3.0 V

0.006 A

VR

I

R = 500 W

The SI unit for electrical resistance is the ohm, W:

1 V1

1 AW

Exercise 2

1. Calculate the current through a circuit when a p.d. of 12 V is applied across a 5Ω resistor.

2. What is the p.d. across a 3Ω resistor when 12mA of current passes through it?

3. How much current flows through a 13kΩresistor when it is connected to a 12V supply?

Resistivity of a Material

The resistivity r is a property of a material that determines its electrical resistance R.

Recalling that R is directly proportional to length L and inversely proportional to area A, we may write:

or L RA

RA L

r r

The unit of resistivity is the ohm-meter (Wm)

Example 3. What length L of copper wire is required to produce a 4 mW resistor? Assume the area of the wire is 7.85 x 10-7 m2 and that the resistivity r of copper is 1.72 x 10-8 W.m .

A = 7.85 x 10-7 m2

LR

Ar

-7 2

-8

(0.004 )(7.85 x 10 m )

1.72 x 10 m

RAL

r

W

W

L = 0.183 mRequired length is:

RESISTIVITIES OF MATERIALS

Material Resistivity values (Ω.m)

Copper 1.72 x 10-8

Constantan 49 x 10-8

Manganin 44 x 10-8

Nichrome 100 x 10-8

Tungsten 55 x 10-8

Electric PowerElectric power P is the rate at which electric energy is used, or work per unit of time.

It is measured in Watts (W)

V q

V

Power = voltage x current

(W) (V) (A)

P = VI I

Also, P = I2R

Using Ohm’s law, we can find electric powerfrom any two of the following parameters: current I, voltage V, and resistance R.

Ohm’s law: V = IR

22; ;

VP VI P I R P

R

Electrical EnergyElectrical energy E is the amount of work that can be done by an EMF. It is measured in Joule (J).

E = Pt

Energy transformed (J) = power (W) x time (s)

Also, Energy = voltage x current x time

E = VIt

Example 5. A power tool is rated at 9 Awhen used with a circuit that provides 120-V.What power is used in operating this tool?

P = VI = (120 V)(9 A) P = 1080 W

Example 6. A 500-W heater draws a current of 10 A. What is the resistance?

R = 5.00 W2

2 2

500 W;

(10 A)

PP I R R

I

Summary of Formulas

QI

t

1C1 A

1 s

Electric current:

; ; V V

I V IR RR I

Ohm’s Law

1 voltResistance: 1 ohm

1 ampere

Summary (Cont.)

or L RA

RA L

r r

22; ;

VP VI P I R P

R

Resistivity of materials:

Electric Power P:

Exercise 3 1. How much power is developed in a battery of EMF 4.5V when a

current of 1.0A is passing through it.

2. A 23kΩ resistor is connected to a 6V EMF supply. Calculate;

a. the current flowing through the resistor.

b. the amount of charge passing through the resistor every 2 minutes.

c. the power dissipated by the EMF supply.

3. A bulb takes a current of 3A from a 12V battery

a. What is the power of the bulb?

b. How much energy is supplied in 10 minutes?

4. How much energy is transferred by a battery of EMF 4.5V when 1.0C of charge passes through it for 2.5 minutes?

REVISION EXERCISE1. When a kettle is plugged into the 230V mains, the current through its element is 10A.

a) What is the resistance of its element?

b) What is the power rating of the element?

c) If the element if made of copper. Copper has a resistivity of 1.72 x 10-8 W.m. If 2m of copper wire is used, calculate its area.

d) How much electrical energy is used when the kettle is switched on for 21/2 hours?

2. If an electric heater takes a current of 4A when connected to a 230V supply, what is its power?

3. If a light bulb has a power of 36W and resistance of 4Ω when connected to a power supply.

a) How much current is flowing through the bulb?

b) Calculate the p.d. across the bulb

4. In 5 seconds, a hairdrier takes 10 000 joules of energy from the mains supply. What is its power in

a) Watts

b) Kilowatts

Thanks!