Question

If a variable frequency ac source is connected to a capacitor then with decrease in frequency the displacement current will

• A. Increase
• B. Decrease
• C. Remains constant
• D. First increase then decrease

Answer 1

Answer: (B)

Decrease

Current through the capacitor is directly proportional to impedance.

$I\propto X_c$

The impedance of a capacitor is $X_c=\frac{1}{\omega C}$

So, $I\propto \frac{1}{\omega C}$

The angular frequency $\omega$ is given as:

$\omega =2\pi f$

$\Rightarrow I\propto \frac{1}{2\pi fC}$

Hence decrease in the frequency $f$ of a.c. source decreases the conduction current.

So there will be a decrease in the displacement current in the circuit.