Question

A coil of self-inductance 2H carries a 2A current. If the direction of current is reversed in 1 second, then find the induced emf.
A. -8V
B. 8V
C. -4V
D. Zero

Answer 1

Hint: In order to solve this question we need to know about the induced emf and the self-inductance of a coil. An emf is said to be induced when a magnet is pushed in and out of the coil. EMFs are of opposite signs that are produced by motion in opposite directions, and by reversing poles EMFs can also be reversed. Self-inductance of a coil is the phenomenon due to which an emf is induced in a coil when the magnetic flux of the coil, linked with the coil changes or current in the coil changes. Now we are able to solve the problem step by step as follows.

Formula Used:
The formula to find the induced emf in a self-inductance coil is given by,
\[E = - L\dfrac{{di}}{{dt}}\]…….. (1)
Where, \[L\] is the self-inductance of the coil and \[\dfrac{{di}}{{dt}}\] is change in current with respect to time.

Complete step by step solution:
To find the induced emf we have from the equation (1)
\[E = - L\dfrac{{di}}{{dt}}\]
\[\Rightarrow \left| E \right| = L\dfrac{{di}}{{dt}}\]
By data, at the beginning the value of current was +2A and after 1sec the direction of the current is reversed, then the current becomes -2A. therefore \[di\]is the change in current can be written as,
\[di = 2 - \left( { - 2} \right)\]
By data, \[L = 2H\], \[i = 2A\] and \[t = 1s\]
\[ \Rightarrow E = 2\left( {\dfrac{{2 - \left( { - 2} \right)}}{1}} \right)\]
\[E = 8V\]
Therefore, the value of induced emf is 8V.

Hence, Option B is the correct answer.

Note:The Self-inductance of a coil depends on the cross-sectional area of the coil, number of turns per unit length in the coil, the length of the solenoid and the permeability of the core material.