Question

There is no resistance in the inductive circuit. Kirchhoff’s voltage law for the circuit is

A. $V + L\dfrac{{di}}{{dt}} = 0$
B. $V = L\dfrac{{di}}{{dt}}$
C. $V - {L^2}\dfrac{{di}}{{dt}} = 0$
D. None of these

Answer 1

Hint We know that if there is no resistance in an R-L circuit then it is a pure inductor connected to the supply. So, it will be a simple L circuit. At first, we will calculate the voltage drop across the inductor. Then we will apply Kirchhoff laws for finding the appropriate expression.

Complete step by step answer
We know that a RL circuit with no resistance behaves as a purely inductive circuit.
So, we will find the voltage drop across the inductor which is $L\dfrac{{di}}{{dt}}$
Now applying Kirchoff's law for the given circuit with no resistance, we get
 $V - L\dfrac{{di}}{{dt}} = 0$
 $V = L\dfrac{{di}}{{dt}}$
Where,
V is the voltage drop across the resistor
Therefore, the Kirchoff law for given circuit is $V = L\dfrac{{di}}{{dt}}$

Hence the correct solution is option B

Additional information
In case of time varying input, the inductor opposes the change in current instantaneously. So, the current in the inductor will fall behind and lag with respect to the original. Also, in the pure inductive circuit the phase shift is 90 degrees on considering sinusoidal input.

Note
In the given question no resistance is assumed while writing the Kirchhoff’s law but there is a small resistance of the inductor too which we have neglected in this question.
The above equation is valid for an alternating current as for direct current it behaves as a short circuit and for that current will be zero and simultaneously the voltage drop will be zero.