Question

Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.

The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______

1. 3.14 cos (314t) V
2. 3.33 sin (314t) V
3. 6.66 cos (314t) V
4. 6.28 cos (314t) V

Answer 1

Correct Answer - Option 3 : 6.66 cos (314t) V

MUTUAL INDUCTION:

If two coils of wire are brought into close proximity with each other so that the magnetic field from one links with the other, a voltage will be generated in the second coil as a result.

This is called mutual induction: when voltage impressed upon one coil induces a voltage in another.

Mutual inductance formula-

V_m = M (dI₁ / dt)

where V_m = voltage induced in the secondary coil

I₁ = is the current flowing in the primary foil

M = mutual inductance

\(M = K\sqrt {W{L^2}} \) 

where K = coupling coefficient

Given:

L₁ = 10 mH

L₂ = 20 mH

K = 0.75

\(M = K\sqrt {W{L^2}} = 0.75\;\sqrt {200} \)

\(= 10.60\;mH = .0106\;H\)

Voltage in the second coil:

 \( {{V_2}} = M\frac{{d{i_1}}}{{dt}} \) 

\(=0 .0106\;\frac{d}{{dt}}2\sin \left( {314} \right)t\;A\;\)

= 6.66 cos (314 t) volt