Question

Consider a series RLC circuit where R = 651 Ω and C = 1.25 μF. However, the inductance L of the inductor is unknown. To find its value, you decide to perform some simple measurements. You apply an ac voltage that peaks at 60.0 V and observe, using an oscilloscope, that the resonance angular frequency occurs at 76300 s–1. What is the inductance of the inductor in millihenrys?

Answer 1

Given,

R = 651 Ohm ; C = 1.25 $\mu$ F ; L = ?

V(max) = 60 V ; f = 76300

Let L be the inductance.

we know that, $\omega$ = 2 pi f = 2 x 3.14 x 76300 = 479164

As the circuit is a series RLC circuit. At resonance frequency:

Xc = X_L

1/ $\omega$ C = $\omega$ L

L = 1/ $\omega$ ²C = 1/ (479164)2 x 1.25 x 10^-6 = 3.48 x 10-6 H

Hence, Inductance = L = 3.48 x 10^-6 H = 0.00348 mH