An RLC circuit is composed of a 100-? resistor, a 10-?F capacitor, and an induct

Question

An RLC circuit is composed of a 100-? resistor, a 10-?F capacitor, and an inductor.

a) If the inductor causes a back-emf of 6 V when the current experiences a change of 6,000 A per second, find the inductance (ignore the minus sign).

b) Find the frequency that would cause the circuit to have a total impedance of 150-?.

c) What frequency will cause the current to be a maximum?

d) What is the value of the current at the resonant frequency (fr) if the AC voltage (rms) is 12 V?

e) What are the values of the total impedance at frequencies of f = 2*fr? At f = (1/2)*fr? Could you have predicted this?

Explanation / Answer

a) emf = L*di/dt

L = 6/6000 = 10^-3 H = 1mH

b) sqrt(R^2+(XL - XC)^2) = 150

XL - XC = 111.8

WL - 1/WC = 111.8

W^2L - 1 = 111.8*WC

W^2*10^-3 - 1 - 0.001118W = 0

W = 32.18

f = W/2pi = 5.12 Hz

c) f = 1/sqrt(L*C) = 1/sqrt(10^-3*10^-6)= 10000 Hz

d) 12/100 = 0.12 A

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