# RLC Circuit: Resonance

An RLC circuit has a capacitance of 0.43 microF.

(a) What inductance will produce a resonance frequency of 95 mHz?

(b) It is desired that the impedance at resonance be 1/2 the impedance at 11 kHz. What value of R should be used to obtain this result?"

Â© BrainMass Inc. brainmass.com October 6, 2022, 1:55 pm ad1c9bdddfhttps://brainmass.com/physics/resonance/rlc-circuit-resonance-38395

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Z =impedance = square root of {R + (X L ^2 -XC^2)}

XL= reactance of inductor = 2 pi f L

XC= reactance of capacitor = 1/ (2 pi f C)

(a) What inductance will produce a resonance frequency of 95 mHz?

At resoance Z = R and XL=XC

2 pi f L = 1/ (2 pi f C)

L = 1/ {C (2pi f ) ^2}

C= 0.00000043 F

f= 95000000 Hz

Therefore L= 6.5E-12 H

(b) It is desired that the impedance at resonance be 1/2 the impedance at 11 kHz. What value of R should be used to obtain this result?"

Impedance at resonance =R

impedance at 11 kHz:

Z =impedance = square root of {R^2+ (X L ^2 -XC^2)}

XL= reactance of inductor = 2 pi f L

XC= reactance of capacitor = 1/ (2 pi f C)

L= 6.5E-12 H

C= 0.00000043 F

f= 11000 Hz

XL= reactance of inductor = 2 pi f L= 0.00000045

XC= reactance of capacitor = 1/ (2 pi f C)= 33.65

At this frequency the reactance of the inductor is negligible

therefore Z= square root of {R^2+ (XC^2)}

For the impedance at resonance to be 1/2 the impedance at 11 kHz

impedance at resonance = R = 1/2square root of {R^2+ (XC^2)}

Squaring both sides

R^2= 1/4 (R^2+ XC^2)

or 3/4 R^2=1/4 (XC^2)

Bur XC= 33.65

Therefore R= 19.43 ohm

https://brainmass.com/physics/resonance/rlc-circuit-resonance-38395