Question

A capacitor becomes a perfect insulator for:
A. alternating current
B. direct current
C. both A and B
D. None of these

Answer 1

Hint:To answer this question, we have to think about the reactance of the capacitor. The resistance offered by the capacitor is known as the reactance of the capacitor. When the reactance of the capacitor is high then, it will behave like an insulator thus not allowing electric current to flow through it. With the help formula for reactance we will determine for which current reactance of the capacitor is high.

Formula Used:
\[{X_c}{\text{ = }}\dfrac{1}{{\omega C}}\]
Where, \[{X_c}\] is known as capacitive reactance of capacitor, \[\omega \] is the frequency of current passing through a capacitor and \[C\] is the capacitance of a capacitor.

Complete step by step answer:
Capacitor is basically used to store the electric charge and it will behave like a capacitor when its reactive become high. We will find the condition for which the reactance of the capacitor is high. We know that the reactance of capacitor is given by relation:
\[{X_c}{\text{ = }}\dfrac{1}{{\omega C}}\]
Also we know that, \[\omega {\text{ = 2}}\pi \nu \], therefore it can be deduced as:
\[{X_c}{\text{ = }}\dfrac{1}{{2\pi \nu C}}\]

For alternating current: We know that the frequency \[\left( \nu \right)\] of alternating current in India is equal to \[50{\text{ Hz}}\]. Therefore the capacitance will be equal to:
\[{X_c}{\text{ = }}\dfrac{1}{{2\pi {\text{ }} \times {\text{ }}50{\text{ }} \times {\text{ }}C}}\]
We can observe that for alternating current there is some finite value of reactance of capacitor.

For direct current: We know that the frequency \[\left( \nu \right)\] of alternating current in India is equal to \[0{\text{ Hz}}\]. Therefore the capacitance will be equal to:
\[{X_c}{\text{ = }}\dfrac{1}{{2\pi {\text{ }} \times {\text{ }}0{\text{ }} \times {\text{ }}C}}\]
\[{X_c}{\text{ = }}\dfrac{1}{{{\text{ }}0{\text{ }}}}{\text{ = }}\infty \]
Thus the reactance or resistance offered by a capacitor when a direct current flows through it is infinite. Hence it will not allow any electric current to flow through it. Therefore it will behave like an insulator. Hence we can say that when direct current is passed through a capacitor then it becomes a perfect insulator for the electric current.

Hence the correct option is B.

Note:Reactance is similar to resistance but when we talk about capacitor and inductor we do not use the term resistance. For capacitors we call it capacitive reactance and for inductors we call it inductive reactance. The frequency of an electric current is the number of cycles of wave it makes in one second. Direct current is a constant in nature.