Asked by EMG
An RLC series circuit has a 2.60 Ω resistor, a 110 µH inductor, and a 70.0 µF capacitor.
(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?
(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?
Answers
Answered by
Damon
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
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
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