Question

1. Answer the following questions:
1. An RLC circuit is used in a radio to tune into an FM station broadcasting at f = 99.7 MHz. The resistance in the circuit is R = 12.6 Ω, and the inductance is L = 1.70 µH. What capacitance should be used?

2. Consider a series RLC circuit with R = 15 ohm, L = 206 mH, C = 75 µF, and a maximum voltage of 147 V.
(a) What is the impedance of the circuit at resonance?
(b) What is the resonance frequency of the circuit?
(c) When will the current be greatest: at resonance, at ten percent below the resonant frequency, or at ten percent above the resonant frequency?
(d) What is the rms current in the circuit at a frequency of 60 Hz?

Answer 1

1) Resonant frequency for parallel or seriel circuits is given by:-

w = 2pi f = sqrt(1/(LC))

2*pi*99.7*10^6 = sqrt(1/(1.7e-6C))

(6.264e8)^2= 1/(1.7e-6C)

C = 1/[(6.264e8)^2*1.7e-6]

= 1.5 *10^-12 F Answer. It does not depend on Resistence