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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