Consider a series LR circuit connected to an ac voltage source given by V_source
ID: 1499977 • Letter: C
Question
Consider a series LR circuit connected to an ac voltage source given by V_source(t) = V_0 cos(omega t). In general the current through resistor R will be of the form I(t) = I_0 cos(omega t - phi), where phi is some phase shift. (Note the minus sign!) (+2) For V_0 = 12 volts and omega = 12 radians/sec, compute the values of I_0 and phi, and clearly state whether phi (using the definition above) is plus or minus. (Read Knight.) (+1) Calculate the time-averaged power supplied to this circuit by the ac voltage source. (Read Knight.)Explanation / Answer
a)
inductive reactance, XL = w*L
= 12*12
= 144 ohms
impedance of the ckt, z = sqrt(r^2 + XL^2)
= sqrt(100^2 + 144^2)
= 175.3 ohms
Io = Vo/z
12/175.3
= 0.068 A
phase angle, phi = tan^-1(-XL/R)
= tan^-1(-144/100)
= 55.2 degrees
b) Average power supplied to the ckt, Pavg = Io^2*R/2
= 0.068^2*100/2
= 0.231 Watts