# The mutual inductance between two coils is 1.25 henry. If the current in the primary changes at the rate of 80 amperes/second, then induced e.m.f in t

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The mutual inductance between two coils is 1.25 henry. If the current in the primary changes at the rate of 80 amperes/second, then induced e.m.f in the secondary is:

1. 12.5 V
2. 64 V
3. 0.016 V
4. 100 V

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Correct Answer - Option 4 : 100 V

Concept:

• Self-inductance: The property of the current-carrying coil to resists the change of current flowing through it.
• This occurs mainly due to the self-induced emf produced in the coil itself.

$⇒ L=N\frac{ϕ}{I}$

Where N = number of turns in the coil, L = self-inductance of the coil, ϕ = flux associated with the coil and I = current in the coil

• Mutual - inductance: Current is induced in secondary coil kept in proximity with the coil carrying current.
• This property of inducing a current in the secondary coil by changing the flux of the secondary coil is called mutal inductance.

$⇒ M =N_{1}\frac{\phi }{I_{2}}$

M is mutual inductance between Coil 2 and 1, N1 is the number of turns in coil 1, ϕ is magnetic flux induced in coil 2.

• The induced emf in the secondary coil is given as

$E = M\frac{di }{dt}$

Calculation:

Given Mutual inductance M = 1. 25 Henery

Rate of change of curren$\frac{di }{dt} = 80$ A

Emf induced E = 1.25 H × 80 A/s = 100 Volt

So, induced emf is 100 V.

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