Question

If the inductance of a coil is 1 henry then its effective resistance in a D.C. circuit will be
${\text{A}}{\text{. }}\infty \\\ {\text{B}}{\text{. zero}} \\\ {\text{C}}{\text{. 1}}\Omega \\\ {\text{D}}{\text{. 2}}\Omega \\\$

Answer 1

The effective resistance offered by an inductor is equal to the product of the frequency of the signal in the circuit and the inductance of the inductor connected to the circuit. We are given the value of the inductance, and by finding out the frequency of direct current we can obtain the required value of the resistance offered by the inductance.

Formula used:
The effective resistance or reactance offered by an inductor having inductance L is given as
${X_L} = \omega L$

Complete answer:
We are given a coil whose inductance is given as
$L = 1H$
This coil is connected to a source of direct current. The direct current is unidirectional in nature and there are no oscillations in the magnitude of the direct current. So, we can write that
$\omega = 0$
Now the reactance offered by an inductance is given as the product of the frequency of the signal and the inductance offered by the coil. It is given as
${X_L} = \omega L$
Inserting the known values of inductance and the frequency of direct current, we get
${X_L} = 0$
Therefore, the effective resistance offered by the inductor to the flow of current is zero and the direct current can flow freely through the inductor without any voltage drop in the inductor.

Hence, the correct answer is option B.

Note:
It should be noted that since an inductor offers zero resistance in a dc circuit, it is utilized in a circuit in which the inductances offer non-zero resistance to the flow of alternating current through them. Analogous to inductors, we have a capacitor which offers infinite resistance to the flow of direct current through itself. Due to these properties, the inductors and conductors are used only in ac circuits and not dc circuits.