Question

In one second, a current of \[10A\] changes through a coil. The induced e.m.f. is \[10V\], then self inductance of the coil is
A) \[2H\]
B) \[5H\]
C) \[1H\]
D) \[0.5H\]

Answer 1

Hint: A changing current through a coil produces a changing flux and hence an emf is induced in the coil which is associated with rate of change or current and self inductance of that coil.

Complete step by step answer:
Step I:
According to Faraday’s law of induced e.m.f, if a conductor is placed in a changing magnetic field in a closed circuit, then an induced current is produced in the conductor. This can be done when an alternating current generates current in another circuit placed nearby.

Step II:
If magnetic flux is also changing due to change in current and induced e.m.f is produced, then this is called self induction. This property of the coil is known as self inductance. Unit of self inductance is Henry (H).

Step III: Given self induced e.m.f., \[e = 10V\]
Rate of change of current, \[\dfrac{{dI}}{{dt}} = \dfrac{{10}}{1} = 10\]
Self inductance of the coil, \[L = ?\]
According to Faraday’s Law of Induced e.m.f.
\[e = L\dfrac{{dI}}{{dt}}\]
Substitute all the values in the equation and calculate the value of self inductance,
\[10 = L.10\]
\[L = \dfrac{{10}}{{10}} = 1H\]

Step IV:
Self inductance of the coil is \[1H\].
Therefore, Option C is the right answer.

Step V:
It is to be noted that if the current in the coil increases, then the self induced e.m.f produced will oppose the rise of the current. But if the value of current decreases in the circuit, the self induced e.m.f will be such that it will support the rise of the current.

Note: It is important to note that the inductance is independent of a system, for example a coil is only dependent on the geometry of the system and the permeability of the medium in which it is placed.