Question

When a particular inductor is connected to a sinusoidal voltage with a 141 V amplitude, a peak current of 8.4 A appears in the inductor. What is the maximum current if the frequency of the applied voltage is doubled? Answer in units of A

What is the inductive reactance at the new frequency? Answer in units of Ω.

Answer 1

The expression for the inductive reactance -

XL = 2 * pi * freq * L
(From above we see that inductive reactance is directly proportional to the frequency)

If the frequency is doubled, then the inductive reactance is doubled.

Reactance (and Impedance) is directly related to the Voltage by Ohm's Law:
V = I * Z ; where Z = R + X, but since R = 0, then Z = X, therefore V = I * X
V = I * X

so we have -

141 V = 8.4 A * X
=> X = 16.79 ohms @ +90 degrees

Now when the frequency of the applied voltage is doubled, reactance will also be doubled. And then the Current *must* go down by HALF.

2X = 33.58 ohms @ +90 degrees

141 V = I * 2X
=> I = 4.2 A

Therefore, the maximum current in this case = 4.2 A

And, inductive reactance at the new frequency = 33.58 ohm.