Question

The currents passing through two inductors of self-inductances 10 mH and 20 mH increase with time at the same rate. Draw graphs showing the variation of:
(I) The magnitude of emf induced with the rate of change of current in each inductor:
(II) The energy stored in each inductor with the current flowing through it:

Answer 1

(I) Magnitude of EMF Induced with Rate of Change of Current:

The induced EMF \( E \) in an inductor is related to the rate of change of current \( \frac{dI}{dt} \) by the formula:

\[ E = L \frac{dI}{dt} \]

where \( L \) is the inductance of the inductor.

Since the rate of change of current \( \frac{dI}{dt} \) is the same for both inductors, the induced EMF is directly proportional to the inductance.

Therefore, the inductor with a larger inductance will have a higher EMF. Specifically, if one inductor has a self
-inductance of 20 mH and the other 10 mH, the EMF in the 20 mH inductor will be twice as large.

The graph of EMF vs. time will show this proportional difference.

(II) Energy Stored in Each Inductor with Current Flowing Through It:

The energy \( W \) stored in an inductor is given by:

\[ W = \frac{1}{2} L I^2 \]

where:

• \( W \) is the energy
• \( L \) is the inductance
• \( I \) is the current

For the same current, the energy stored is directly proportional to the inductance. Thus, the inductor with 20 mH stores twice the energy as the 10 mH inductor.

The graph of energy vs. current will show a quadratic relationship, with the curve for the larger inductance always being higher by a factor of 2 for the same current.