Question

An ac source is connected to a capacitor C. Due to decrease in its operating frequency:

• A. capacitive reactance remains constant
• B. capacitive reactance decreases
• C. displacement current increases
• D. displacement current decreases

Answer 1

Answer: (D)

displacement current decreases

Answer 2

The correct option is (D): displacement current decreases When an AC source is connected to a capacitor, the capacitive reactance (Xc) is given by:

$X_c=\frac{1}{(2\times\pi\times f \times C)}$

where: f is the frequency of the AC source C is the capacitance of the capacitor

As we can see from the above equation, the capacitive reactance is inversely proportional to the frequency of the AC source.

So, if the frequency of the AC source decreases, the capacitive reactance will increase.

Therefore, the statement "capacitive reactance remains constant" is not correct.

The statement "capacitive reactance decreases" is also not correct.

The statement "displacement current increases" is also not correct because the displacement current in a capacitor is directly proportional to the rate of change of the electric field, which is not affected by the frequency of the AC source.

Therefore, the correct answer is: "displacement current decreases". The displacement current in a capacitor is given by:

$I_d=C\times\frac{dV}{dt}$

where: Id is the displacement current C is the capacitance of the capacitor $\frac{dV}{dt}$ is the rate of change of the voltage across the capacitor

As the frequency of the AC source decreases, the rate of change of voltage across the capacitor decreases, which in turn decreases the displacement current.