Question

A 24.0-mH inductor has a reactance of 1.80 k?.

(a) What is the frequency of the ac current that passes through the inductor?
Hz

(b) What is the capacitance of a capacitor that has the same reactance at this frequency?
F

(c) The frequency is tripled, so that the reactances of the inductor and capacitor are no longer equal. What is the new reactance of the inductor?
k?

(d) What is the new reactance of the capacitor?

Answer 1

a)

L = 24 mH = 0.024 H

Reactance, Xl = 1.8 k ohm= 1800 ohm = 2*pi*f*L

So, f = 1800/(2*pi*L) = 1800/(2*pi*0.024) = 1.19*10^4 Hz <-------answer

b)

Xc = 1800 ohm

f = 1.19*!0^4 Hz

But, Xc = 1/(2*pi*f*C) = 1800

So, C = 1/(2*pi*1.14*10^-4*1800) = 7.41*10^-9 F <-------answer

c)

f = 3*1.19*10^4 = 3.57*10^4 Hz

new reactance of inductor, Xl' = 2*pi*f*L = 2*pi*3.57*10^4*0.024 = 5383.4 ohm = 5.38 k ohm

d)

New Capacitive reactance, Xc' = 1/(2*pi*f*C) = 1/(2*pi*3.57*10^4*7.41*10^-9) = 601.6 ohm