Question

23. A 10mH inductor that has 512 of resistance is hooked to 12V battery source for 5ms. What is the characteristic time constant, and the current at that time? 24. An RLC series circuit has a 10.0012, a 10.00mH inductor, and a 10.00uF capacitor, and has a 10V source. a. Find the circuit's impedance and current at 100 Hz. b. Find the resonant frequency of the circuit and the average power dissipated at resonance.

Answer 1

23)

given

inductance L = 10*10^-3 H

resisatcne R = 5 ohm

voltage v = 12 V

charecteristic time T = L/R= 10^-2/5 = 2 ms

current i = i max(1-exp(-t/T))

i = (12/5)(1-exp(-5/2)) = 2.203 A

24)

a) inductive reactance xL = wL = 2*3.14*100*1/100 = 6.28 ohm

capacitive reactance xc = 1/2*3.14*100*10*10^-6 = 159.15 ohm

impedance z = sqrt((159.23-6.28)^2+10^2) = 153.19 ohm

current i = 10/153.19 = 0.065 A

b)

resonant frequency f =1/2*3.14*sqrt(LC) =  1/2*3.14*sqrt(10*10^-3*10*10^-6) = 503.6 Hz

AVERAGE POWER P AVG = Vrms^2/R = 10^2/10 = 10 W