In a car spark-coil, when the current in the primary is reduced from $4.0 A$ to $zero$ in $10 μ s$ , an emf of $40, 000 V$ is induced in the secondary coil. Find the mutual inductance $M$ of the primary and the secondary windings of the spark coil.

0.2 H

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0.1 H

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0.3 H

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None

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Solution

The correct option is B $0.1 H$
The magnitude of induced emf in secondary coil is given by:
$| ε | = M ∣ ∣ ∣ \frac{d i}{d t} ∣ ∣ ∣ . . . (i)$
where $M =$ mutual inductance between primary and secondary coils/windings.
given $ε = 40, 000 V$ and
$∣ ∣ ∣ \frac{d i}{d t} ∣ ∣ ∣ = \frac{(4 - 0) A}{10 \times 10^{- 6} s} = 4 \times 10^{5} A/s$
From Eq $(i)$ ,
$M = \frac{40000}{4 \times 10^{5}}$
$∴ M = \frac{1}{10} = 0.1 H$

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In a car spark-coil, when the current in the primary is reduced from 4.0 A to zero in 10 μs, an emf of 40,000 V is induced in the secondary coil. Find the mutual inductance M of the primary and the secondary windings of the spark coil.

In a car spark-coil, when the current in the primary is reduced from $4.0 A$ to $zero$ in $10 μ s$ , an emf of $40, 000 V$ is induced in the secondary coil. Find the mutual inductance $M$ of the primary and the secondary windings of the spark coil.