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## Homework Statement

A series RLC circuit has R=75 ohms, C=20 mF and a resonance frequency of 5.0 kHz. (i) What is the value of inductance? (ii)What is the impedance of the circuit at residence? (iii)What is the rms current at resonance if the rms voltage of the power supply is 120 V? (iv) How much average power is consumed in the circuit at resonance?

## Homework Equations

f=1/(2π√LC), z= √(XL-XC)^2 +R^2, I=V/Z and P=VI [/B]

## The Attempt at a Solution

(i) What is the value of inductance?

f=1/(2π√LC)

L=1/4π^2 * 1/f^2C

1/(4π^2) * 1/[(50e3)^2(20^-6)]

L=5.07 e-7 H

(ii)What is the impedance of the circuit at residence?

z= √(XL-XC)^2 +R^2

z= √WL-1/WC)^2 +R^2

z= √[(314e3 * 5.07e-7)-(1/314e3 * 20e-6)]^2 +5^2

z= 75 Ohms

(iii)What is the rms current at resonance if the rms voltage of the power supply is 120 V?

I=V/Z

I=120/75

I=1.6 A

(iv) How much average power is consumed in the circuit at resonance?

P=VI

P=120* 1.8

P=192 W[/B]