In a purely inductive AC circuit, L = 23.0 mH and the rms voltage is 220 V. Calc

Question

In a purely inductive AC circuit, L = 23.0 mH and the rms voltage is 220 V. Calculate the inductive reactance and rms current in the circuit if the frequency is 60.0 Hz.

SOLVE IT

Conceptualize The figure shows the physical situation for this problem.

Categorize We evaluate the reactance and the current from equations developed in this section, so we categorize this example as a substitution problem.

Use the following equation to find the inductive reactance:

XL = ?L = 2?f L

Use an rms version of the equation for the maximum current in an inductor to find the rms current:

What if the frequency is now 600 Hz, and the maximum voltage (not rms) is 220 V? Find the rms current in the circuit.

Explanation / Answer

L=23mH=23*10^-3 H
f=60 Hz
Vrms=220 v

1)
inductive reactance XL=WL=2pi*f*L
=2*3.14*60*23*10^-3
=8.6664 ohm or ?

2)
Irms=Vrms/XL
=220/8.6664
=25.38 Ampere

3)
Vmax=220
Vrms=Vmax/sqrt(2)
=220/1.414
=155.56 V
===>
Irms=Vrms/XL
=155.56/8.6664
=17.95 Ampere

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