Question

An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 43.8 H inductor, determine the inductive reactance and the rms current through the inductor.

Answer 1

The reactance of an inductor is given by:

X = 2πfL

X is the inductor's reactance

f is the frequency of the supplied voltage

L is the inductor's inductance

The given values are:

f = 60.0Hz

L = 43.8mH (I'm assuming the value is given in milli Henries because this is within the normal range of inductors)

Plug these values in and solve for X:

X = 2π(60.0)(43.8×10⁻³)

X = 16.512Ω

Round this value to 3 significant figures:

X = 16.5Ω

The relationship between AC voltage and current is given by:

V = IZ

V is the voltage

I is the current

Z is the impedance

For an AC inductor circuit, Z = X = 16.512Ω and V is the rms voltage 120V. Plug these values in to get the rms current:

120 = I×16.512

I = 7.2673A

Round this value to 3 significant figures:

I = 7.27A