Alternating Current

Physics 102Professor Lee

CarknerLecture 23

PAL #22 RL Circuits

Solenoid: 5 cm long, 1 cm diameter 0.1 V of emf is induced by increasing

the current from 0 to 3 A in 0.5 seconds = -L(I/t) L = t/I = [(0.1)(0.5)]/(3)= L = 0N2A/l

N = (Ll/0A)½

N = [(0.0167)(0.05) / (4X10-7)()(0.005)2]½ N =

A switch is closed, starting a clockwise current in a circuit. What direction is the magnetic field through the middle of the loop? What direction is the current induced by this magnetic field?

A) Up, clockwiseB) Down, clockwiseC) Up, counterclockwiseD) Down, counterclockwiseE) No magnetic field is produced

The switch is now opened, stopping the clockwise current flow. Is there a self-induced current in the loop now?

A) No, since the magnetic field goes to zero

B) No, self induction only works with constant currents

C) Yes, the decreasing B field produces a clockwise current

D) Yes, the decreasing B field produces a counterclockwise current

E) Yes, it runs first clockwise then counterclockwise

To step down 120 household current to 12 volts, we would need a transformer with a ratio of turns between the primary and secondary transformer of,

A) 1 to 1B) 10 to 1C) 12 to 1D) 100 to 1E) 120 to 1

Sine Wave = angular frequency = number of radians per second

f = frequency = number of cycles per second

T = period = time for one cycle

1 cycle = 2 radians

f = /2

T = 1/f = 2/

¼ cycle

t = ¼ T

/2 rad.

½ cycle

t = ½ T

rad.

¾ cycle

t = ¾ T

/2 rad.

AC vs. DC Voltage and current vary sinusoidally with time

Voltage and current will have a frequency and

angular frequency in radians per second

Capacitors and inductors can produce resistance-like effects

Circuits have natural oscillation frequencies May get resonance

V and I in Phase

Time Dependence

The current and voltage values vary with time

But, the variation follows a known pattern sine wave

We can discuss certain key values Namely,

The maximum value (Vmax, Imax)

Can think of as an average

Max Values

The value at any time is just the maximum value times the sinusoidal factor: V = Vmax sint I = Imax sint

Note: Ohm’s Law still holds

rms Values Since the current varies in a systematic

manner we would like to have some sort of average value However the average of a sinusoidal variation is

0

Since power depends on I2 (P =I2R) it does not care if the current is positive or negative

Finding rms

rms Current and Voltage We can write the rms (root mean squared)

current as:Irms = Imax/(2)½ = 0.707 Imax

We can write a similar relationship for the voltage

Vrms = Vmax/(2)½ = 0.707 Vmax

e.g. Vmax = Imax R and Vrms = IrmsR

Resistors and AC

We can use Ohm’s law in an AC circuit with a resistor

The current and the potential difference are in phase

Large V produces large current

AC Circuit with Resistor

Today’s PAL

Consider a AC circuit with a 240 resistance lightbulb connected to Vrms = 120 V, 60 Hz household current.

For the lightbulb, what is: the rms current the maximum current the maximum power the average (rms) power the power at time equals 1/120 second

Capacitors and AC Consider a capacitor connected to an AC voltage

source

When the current changes direction it moves the charge back and decreases the voltage

The capacitor is constantly being charged and discharged

In a AC circuit the current will vary with some average rms value that depends on the voltage and the capacitance

Capacitor acts as a resistor

AC Circuit with Capacitor

Reactance The capacitor impedes the flow of the current

XC = 1/(C) The reactance, current and voltage across the

capacitor are related by:VC = IXC

At high frequency the capacitor never gets much charge on it

The voltage and the current across the capacitor are not in phase

Phase

The voltage and current across the capacitor are offset

Since the capacitor offers no resistance As voltage increases current decreases

We say the voltage lags the current by 90 degrees Voltage and current are offset by 1/4 cycle

AC Capacitor Phase Lag

Capacitor Power

Since P = VI, we can see if the power is positive or negative based on the sign of I and V

P is positive half the time and negative half the time

The capacitor draws energy from and returns energy to the generator in equal measure

Next Time

Read 21.13 Homework: Ch 21, P 58, 60, 61, 62