Question

Two ac generators supply the same voltage. However, the first generator has a frequency of 1.2 kHz, and the second has a frequency of 4.6 kHz. When an inductor is connected across the terminals of the first generator, the current delivered is 0.56 A. How much current is delivered when this inductor is connected across the terminals of the second generator? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise

Answer 1

I_2 = 0.146 A

Step-by-step explanation:

The formula for current in an inductor is;

I_rms = V_rms/X_L

Where X_L is inductance wirh formula 2πfL

So, I_rms = V_rms/X_L

Applying this to the two generators, we have;

First generator;

I_1 = V_rms/(2π(f_1)L)

And I_2 = V_rms/(2π(f_2)L)

Thus, to find the current in the second generator, we divide eq 1 by eq 2;

So,

I_2/I_1 = [V_rms/(2π(f_2)L)]/[V_rms/(2π(f_1)L)]

Some values will cance out leaving us with;

I_2/I_1 = f_1/f_2

I_2 = I_1(f_1/f_2)

Plugging in the relevant values ;

I_2 = 0.56(1.2/4.6)

I_2 = 0.146 A