An RLC series circuit has a 2.60 Ω resistor, a 110 µH inductor, and a 70.0 µF capacitor.

Question

(a) Find the circuit's impedance (in Ω) at 120 Hz.
(b) Find the circuit's impedance (in Ω) at 5.00 kHz.
(c) If the voltage source has Vrms = 5.60 V, what is Irms (in A) at each frequency?
(d) What is the resonant frequency (in kHz) of the circuit?
(e) What is Irms (in A) at resonance?

Answer 1

w = 2 pi f
impedance = sqrt [ R^2 + (wL-1/wC)^2 ]
if f = 120 Hz, w = 2 pi f = 754
impedance = sqrt [2.6^2 + (754*110*10^-6 - 1/754*70*10^-6 )^2]

repeat for new f

i = V/impedance = 5.6/impedance

at resonance w = 2 pi f = 1/sqrt(LC)
then
impedance = sqt [ R^2 + ( sqrt L/C - sqrt L/C)^2) ] = R
so i = V/R

Answer 2

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Answer 3

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Answer 4

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