Power and AC

Energy Transformation

Electric energy can be transformed into other more useful forms

Power is the rate of energy transformation P = ΔPE/t ΔPE = QV P = QV/ t I = Q/ t P = IV units – Watt (W)

Example

What is the resistance of a 40 W car headlight designed for a 12V car battery?

KiloWatt - Hour

Electric companies charge by the amount of energy used

Larger unit than Joule is used – called the kilowatt-hour (kW•hr)

1 kW•hr = 3.6 x 106 J

Example

A heater draws 15.0A on a 120V line. How much power does it use and how much does it cost per month (30 days) to operate if it runs 3.0 hours per day and the electric company charges 10.5 cents per kW•hr?

Example

A lightning bolt transfers 109 J of energy across a potential difference of 5 x 107V in .2 s. Find the charge transferred, the current, and the power of the bolt.

Overload

All wires have resistance and some of the electric energy is changed to heat

Overload is when wire carries more than the safe amount of current

Fuses and circuit breakers protect from overload

Causes of overload: too many devices drawing too much current, “short” which is crossed wiring

Example

A 100W lightbulb, 1800W heater, 350W stereo, and 1200W television are all connected to the same circuit which has a 20A fuse. Can all of these be operating at the same time?

Alternating Current (AC)

Direct current (DC) is produced from a battery – flows steadily in one direction

Electric generating plants produce AC current – this reverses direction many times per second

ACDC

Sinusoidal Nature

Current and voltage produced in AC are sinusoidal

V = Vosin 2πft

I = Io sin 2πft

Vo and Io are called peak voltage and current

F is the frequency of oscillation (60 Hz)

Power

Even though average current is zero, power is always delivered

P = Io2R

Since Io is squared, power is always +

Average Current, Voltage, Power

Root mean square averages These are the average current, voltage,

and power delivered by an ac line Iavg = .5 Io

2 = .707 Io

Vavg = .707 Vo

Pavg = (Vavg)2/ R

Pavg = (Iavg)2R

Examples

What is the peak voltage of a 120V ac line?

A stereo receiver is capable of average power output of 100W into an 8Ω loudspeaker. What is the rms voltage and rms current fed to the speaker a) at max power of 100W and b) at 1.0 W