Ohm’s LawOhm’s LawOhm’s LawOhm’s Law

Physics

Dr. Robert MacKay

Voltage (Volts)Electrical Pressure

+

-

+-

V

Current (Amps)Current (Amps)Charge FlowCharge Flow

Current (Amps)Current (Amps)Charge FlowCharge Flow

+ +

+-

++ + + + +

+ +

I

V

Resistance, R (Ohms, Resistance, R (Ohms, Ω))ImpedenceImpedence

Resistance, R (Ohms, Resistance, R (Ohms, Ω))ImpedenceImpedence

- -

+-

-- - - - -

- -

I

VR Depends on Temperature Material of wire Area of wire Length of wire

Resistance, R (Ohms, Resistance, R (Ohms, Ω))ImpedenceImpedence

Resistance, R (Ohms, Resistance, R (Ohms, Ω))ImpedenceImpedence

- - -- - - - -

- -

R Depends on: * Temperature * Material of wire * Cros sectional Area * Length

Area

Length

Resistance and ResistivityResistance and ResistivityResistance and ResistivityResistance and Resistivity

R L

A

= resistivityR=resistance

Material (ž- m) (°C-1)Silver 1.59x10-8 6.1x10-3

Copper 1.70x10-8 6.8x10-3

Carbon 3.6x10-5 -5.0x10-4

Silicon 2.5x102 -7.0x10-2

Glass 1012

Rubber 1015 1

R R0T

R R0(1T)

0T

0(1T)

As a wire heats it up its resistance increases.

Some thermometers work on this principle.

Ohm’s LawOhm’s LawV= I RV= I R

Ohm’s LawOhm’s LawV= I RV= I R

- -

+-

-- - - - -

- -

I

V

ExerciseExerciseExerciseExercise Find the electric voltage required to have

10 Amps of current flow through a 2 Ω resistor.

Given: I= 10 A and R=2 Ω Wanted: V Solution: V=I R V= (10 A) (2 Ω) = 20 Volts

ExerciseExerciseExerciseExercise Find the electric current flowing in a 10 Ω

resistor (light bulb) when connected to a 20 Volt battery.

Given: V= 20 Vand R=10 Ω Wanted: I Solution: V=I R or I=V / R I= (20 V) / (10 Ω) = 2 Amps

ExerciseExerciseExerciseExercise When a 60 Volt battery is connected to a

circuit 4.0 amps of current flow from the battery. What is the circuit’s resistance.

Given: V= 60 V and I=4.0 Amps Wanted: R Solution: V=I R or R=V / I I= (60 V) / (4.0 Amps) = 15 Ω

Electric Power (Watts)Electric Power (Watts)

Power = Current x Voltage 1 Watt = Amp x Volt

CurcuitsCurcuitsR=10 Ω

A

V= 20 V

I =?P= ?

R

I

V

P

10 Ω

20 V

CurcuitsCurcuitsR=10 Ω

A

V= 20 V

I =?P= ?

R

I

V

P

10 Ω

20 V

2.0 A

V= I RorI = V / R

CurcuitsCurcuitsR=10 Ω

A

V= 20 V

I =?P= ?

R

I

V

P

10 Ω

20 V

2.0 Amps

40.0 Watts

P= I V = 2A(20V) = 40W

V= I RorI = V / R

CurcuitsCurcuitsR=?

A

V= 120 V

I =?P= 60 W

R

I

V

P

120 V

60 W

CurcuitsCurcuitsR=?

A

V= 120 V

I =?P= 60 W

R

I

V

P

120 V

60 W

V= I R

P= I V or I=P/V=60W/120V=0.5A

CurcuitsCurcuitsR=?

A

V= 120 V

I =?P= 60 W

R

I

V

P

120 V

60 W

0.50A

CurcuitsCurcuitsR=?

A

V= 120 V

I =?P= 60 W

R

I

V

P

120 V

60 W

0.50A

R=V/I=120V/0.5A=240

CurcuitsCurcuitsR=?

A

V= 120 V

I =?P= 60 W

R

I

V

P

120 V

60 W

0.50A

240

CurcuitsCurcuitsR=10 Ω

A

V= 20 V

I =2 A

P= 40 Watts

R

I

V

P

10 Ω

20 V

2 A

40 Watts

Two light bulbs are connected in series to a battery the resistance of each is 20 . What is the total effective resistance of this series combination?

Two light bulbs are connected in series to a battery the resistance of each is 20 . What is the total effective resistance of this series combination?

Req=R1+R2= 20 20 40

Two light bulbs are connected in series to a 40 Volt battery. The resistance of each is 20 . What is the total Current leaving the battery?

Two light bulbs are connected in series to a 40 Volt battery. The resistance of each is 20 . What is the total Current leaving the battery?

V=I R or I=V/R (R=Req=40

I=40V/40 =1.0 Amp

CurcuitsCurcuitsR=10 Ω

A

V= 20 V

I =2 A

P= 40 Watts

R

I

V

P

10 Ω

20 V

2 A

40 Watts

A bit of triviaA bit of trivia When 2 equal resistors are connected in parallel the effective

resistance is half the value of each. (two 10 resistor Req=5) When 3 equal resistors are connected in parallel the effective

resistance is one-third the value of each. (three10 resistor Req=3.33)

When 4 equal resistors are connected in parallel the effective resistance is one-forth the value of each. (four10 resistor Req=2.5)

When N equal resistors are connected in parallel the effective resistance is 1/N the value of each. (N 10 resistor Req=10/N)

What is the effective total resistance when 10 equal 10 resistors are connected in parallel?

What is the effective total resistance when 10 equal 10 resistors are connected in parallel?

Req=10/10=1.0

Two 20 Resistors are connected in parallel to a 20 V battery. What is the voltage difference across each resistor?

Two 20 Resistors are connected in parallel to a 20 V battery. What is the voltage difference across each resistor?

V=V1=V2=20 V

Two 20 Resistors are connected in parallel to a 20 V battery. What is the current flowing through each resistor?

Two 20 Resistors are connected in parallel to a 20 V battery. What is the voltage difference across each resistor?

I=V/R I1=V1/R1 and I2=V2/R2

I1=20V/ 20 =1.0 A

I2=20V/ 20 =1.0 A

Two 20 Resistors are connected in parallel to a 20 V battery. What is the total effective resistance of this circuit?

Two 20 Resistors are connected in parallel to a 20 V battery. What is the current flowing through each resistor?

R=V/I=20V/2.0A=10