Question

This question has 3 parts. A single loop RLC Circuit has resistance 5.12 Ω, a capacitance 19.3µF, and inductance 998 mH. The power supply has a peak value of 31.3 V. (a) At what angular frequency (in rad/s) will the current have it’s maximum value?

(c) At what angular frequency (in rad/s) will the current amplitude have one-half of this maximum value?

Answer 1

Current will be maximum when impedence of circuit will be minimum

Let,

R be resistance

C be capacitance

L be inductance

w is angular velocity

So impedence 'Z' of circuit is given by

Z=√{R² +(wL - 1/wC) ²}

Impedence will be minimum when

wL =1/wC

w=√(1/LC) =227.85

c)

Maximum current = V/R

Current amplitude will be one half when impedence of circuit is 2R

√{ R² +(wL- 1/wC) ²} = 2R

So,

3R² = ±( wL - 1/wC)

Solving eqn

w²L - 1/C - 3wR² =0

w= 270.64 , -191. 84

Solving second eqn

w²L - 1/C + 3wR² =0

w= 191.84 , -270. 64

Value of angular frequency

w= 279.64 rad/s

w= 191.84 rad/s