Answer to Question #91642 in Electric Circuits for Lawunn Khaing

Question

When a particular inductor is connected to a source of
sinusoidally varying emf with constant amplitude and a fre
quency of 60.0 Hz, the rms current is 3.00 A. What is the
rms current if the source frequency is doubled? (a) 12.0 A
(b) 6.00 A (c) 4.24 A (d) 3.00 A (e) 1.50 A (ii) Repeat part
(i) assuming the load is a capacitor instead of an inductor.
(iii) Repeat part (i) assuming the load is a resistor instead
of an inductor.

Answer 1

The current in an AC circuit with some reactive element such as an inductor or capacitor with impedance Z (or reactance X) can be expressed through Ohm's law:

$$I=\frac{U}{X}.$$

The reactance of the inductor is

$$X_L=\omega L,$$

Capacitor

$$X_C=\frac{1}{\omega C}.$$

The resistance of a resistor does not depend on frequency.

So if the frequency is doubled, according to the first equation the current will reduce twice and will be 1.5 A.

If we replace the inductor with the capacitor, the currency will increase twice to 6 A.

In case of using the resistor nothing will change for the current and it will remain the same.