A current in a coil of inductance 5 H decreases at a rate of 2 Amp/sec. The induced emf is

CONCEPT:

Self-Induction:

• Whenever the electric current passing through a coil changes, the magnetic flux linked with it will also change.
• As a result of this, in accordance with Faraday’s laws of electromagnetic induction, an emf is induced in the coil which opposes the change that causes it.
• This phenomenon is called ‘self-induction’ and the emf induced is called back emf, current so produced in the coil is called induced current.
• Self-inductance of a solenoid is given by –

\(L=\frac{{{\mu }_{o}}{{N}^{2}}A}{l}\)

Where μo = Absolute permeability, N = Number of turns, l = length of the solenoid, the resistance of the coil (R) = 4Ω, and A = Area of the solenoid.

Induced e.m.f can be given as,

\(⇒ e =- L\frac{{di}}{{dt}}\)

CALCULATION:

Given -

di/dt = -2 Amp/sec and L = 5 H (Since the current decreases at a rate of 2 Amp/sec).

The emf induced across the inductor is,

\(⇒ e =- L\frac{{di}}{{dt}}=-(5\times (-2) )=10\, V\)