Question

The reactance of a capacitor connected with D.C. voltage is?
(A) Zero
(B) Infinity
(C)$1\Omega$
(D) None of these

Answer 1

Hint The frequency of a circuit is the number of times current changes its direction in a second. For a D.C. voltage circuit frequency of the circuit is zero as the direction of flow of electrons i.e. current always remains the same but for an A.C. circuit, the frequency of the circuit is not zero as the direction of current keeps changing.
Formula used
${X_c} = \dfrac{1}{{\omega C}}$
$\omega = 2\pi f$
Where$\omega$ is the angular frequency of the circuit, ${X_c}$is the capacitive reactance of the circuit, $C$is the capacitance of the capacitor,$f$ if the frequency of the circuit.

Complete Step-by-step solution
We know that,
The frequency of a circuit is the number of times current changes its direction in a second.
${X_c} = \dfrac{1}{{\omega C}}$
$\omega = 2\pi f$
Where$\omega$ is the angular frequency of the circuit, ${X_c}$is the capacitive reactance of the circuit, $C$is the capacitance of the capacitor,$f$ if the frequency of the circuit.
$\Rightarrow {X_c} = \dfrac{1}{{2\pi fC}}$
As for a D.C. voltage circuit frequency of the circuit is zero as the direction of flow of electrons.
$\Rightarrow f = 0Hz$
$\Rightarrow {X_c} = \dfrac{1}{{2\pi \times 0 \times C}}$
$\Rightarrow {X_c} = \infty \Omega$

Hence the correct answer to the above question is (B) Infinity.

Additional information
Like in the A.C. circuit the resistance provided by a capacitor is called capacitive reactance or reactance of a capacitor. Similarly, the resistance provided by the inductor is called inductive reactance or reactance of an inductor.

Note
If the circuit would have been an alternating current circuit i.e. an A.C. circuit then the circuit would have a non-zero frequency. Then in such a case, we have to enter the given values of capacitance and frequency and calculate the capacitive reactance of the circuit. The S.I unit of capacitive reactance is also ohms.