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Question: In a coil of self-inductance of 5 henry, the rate of change of current is 2 ampere per second, the e...

In a coil of self-inductance of 5 henry, the rate of change of current is 2 ampere per second, the e.m.f induced in the coil is
A. 5V
B. – 5V
C. – 10V
D. 10V

Explanation

Solution

To solve this problem, we need to apply the Faraday’s law of electromagnetic induction, which states that whenever there is a change in the magnetic flux linked with the coil, an emf is induced across its ends.
Emf, ε=−dϕdt\varepsilon = - \dfrac{{d\phi }}{{dt}}
where ϕ\phi = magnetic flux linked with the coil.

Complete step by step solution:
The Faraday’s law of electromagnetic induction tells us that the magnetic energy can be converted to electric energy that –
When there is a change in the magnetic flux linked with the coil, an emf is induced across its ends.
Emf, ε=−dϕdt\varepsilon = - \dfrac{{d\phi }}{{dt}}
This negative sign indicates that the emf produced by the magnetic field creates an effect so as to nullify the magnetic field that is giving rise to the emf.
An inductor is a passive conductor which consists of a conductor wound around an object, which is called the core. It is used to store the magnetic energy when the electric current flows through it.
When DC flows through an inductor, it behaves as a normal conductor. But, when AC flows through an inductor, there occurs a phenomenon called self-inductance.
The self-inductance is a phenomenon by which there is an emf produced in the inductor, called the back emf, which produces a magnetic field to oppose the flow of alternating current flowing through it.
Mathematically,
We know,
ε=−dϕdt\varepsilon = - \dfrac{{d\phi }}{{dt}}

Since, the flux generated is directly proportional to the alternating current flowing through the coil, we get –
ε∝−dIdt\varepsilon \propto - \dfrac{{dI}}{{dt}}
where I = the current flowing through the coil.
By introducing a constant,
ε=−LdIdt\varepsilon = - L\dfrac{{dI}}{{dt}}
The constant L is termed as the coefficient of self-inductance or simply, inductance. The unit is henry (H).
Given,
Inductance of the coil, L=5HL = 5H
Rate of change of current, dIdt=2As−1\dfrac{{dI}}{{dt}} = 2A{s^{ - 1}}
Substituting, we get –
ε=−5×2=−10V\varepsilon = - 5 \times 2 = - 10V

Hence, the correct option is Option C.

Note: The reason for adding the negative sign is based on a rule called Lenz law, which states that, direction of the electric current, induced in a conductor by the changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.