Three coaxial coils are wound on the same soft-iron core

PHYSICS · Multi-part · CBSE · Physics · Electromagnetic Induction · Electromagnetic Induction

Problem

Three coaxial coils are wound on the same soft-iron core. The primary coil

P

is fed by a current

I_p = 10\,e^{-25t}\,\text{A}

(where

t

is in seconds). The secondary coils

S_1

and

S_2

are sufficiently far apart on the core so that they do not couple with each other directly. Their mutual inductances with the primary are

M_1 = 0.30\,\text{H}

and

M_2 = 0.20\,\text{H}

, respectively. (i) Derive expressions for the emfs induced in

S_1

and

S_2

as functions of time. (ii) The two secondary coils are connected in series so that their emfs aid each other. Write the expression for the net induced emf and calculate its magnitude at

t = 0.020\,\text{s}

. (iii) If a

10\,\Omega

resistor is connected across the series combination of

S_1

and

S_2

, compute the instantaneous current through the resistor at

t = 0.020\,\text{s}

and state its direction with respect to the current in the primary.

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