Electrical Work and PowerElectrical Work and Power

Electrical Work and PowerElectrical Work and Power

I I+ -Higher V1

Lower V2

Resistance R

Current I flows through a potential difference V

Follow a charge Q : at positive end, U1 = QV1

at negative end, U2 = QV2

P.E. Decreases: 0U Q V

The speed of the charges is constant in the wires and resistor.

What is electrical potential energy converted to?

Electrical resistance converts electrical potential energy to thermal energy (heat), just as friction in mechanical systems converts mechanical energy to heat.

This thermal energy means the atoms in theconductor move faster and so the conductor getshotter.The average kinetic energy of the electrons doesn’t increase once the current reaches a steady state; the electrons lose energy in collisions with the atoms as fast as it is supplied by the field.

Power dissipated by a resistor:Power dissipated by a resistor:

( )

U Q VP IV

t t

Power dissipated= current x potential difference

Units: 1 volt (=J/C) x 1 amp (=C/s) = 1 watt (= 1 J/s)

For Resistor: V = IR, so there are 2 other equivalent formulas:

This power dissipated is called “Joule heating” in a resistor

2

2 VP VI I R

R

ExampleExample

a) What is the resistance of a “60 watt” bulb? (for a 120-V supply)

b) Find R for a 60-W headlamp (12-V battery).

c) What power do you get from a “60-W” household bulb if you connect it to a 12-V car battery?

Example Example

The tungsten filament of a light bulb dissipates 60.0W of power from a 120-volt source. If the filament is a wire 50.0 mm long and 0.250 mm in diameter, calculate the resistivity of tungsten at the operating temperature of the filament.

Quiz

Car batteries are usually rated in ampere-hours. This information designate the amount of:

a) currentb) powerc) energyd) chargee) potential that the battery can supply

““Electromotive force Electromotive force εε ” (emf)” (emf)

Units: J/C = volts (not actually a force) but it “pushes” the charges through the circuit.

Eg: Battery (chemical energy electrical energy) Generator (mechanical energy electrical energy)

ε external work per unit charge

- +

I

ε=12 V R

I = 2 A

What does the energy balance look like in this circuit?

When current leaves the batterythe battery supplies powerequal to:

If current were forced to enterthe battery, (as in charging it)then it absorbs the same power

P = Iε = 24W

2126 so Joule heating=I 24

2V

R R WA

Resistor: Electrical energy heat

Real BatteriesReal Batteries

RL (external resistance, “load”)

r = “internal resistance” of the battery

B

A

r

I

I

I

VB + -Ir=VA

VA – VB = V = “terminal voltage” measured

( )A B

Ir V V “Terminal voltage”

ε - Ir = V

ExampleExample

A battery has an emf of 12V and an internal resistance of 0.05Ω. Its terminals are connected to a load resistance of 3Ω. Find:

a) The current in the circuit and the terminal voltage

b) The power dissipated in the load, the internal resistance, and the total power delivered by the battery

ExampleExampleShow that the maximum power lost in the load resistance R

occurs when R=r, that is, when the load resistance matches the internal resistance of the battery.

ExampleExample Automobile battery:

12.8 V (with 20 A current) 9.2 V (with 200 A current)

Find: E and rinternal of battery

At terminals

Shocking questionsShocking questions- Why is it safer to touch wires with the back of your hand?

- If you fall from a building and on your way down grab a high-voltage line, will you be electrocuted?