Question

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

• A. $0.2\text{H}$
• B. $0.1\text{H}$
• C. $0.3\text{H}$
• D. None

Answer 1

The correct option is B $0.1\text{H}$

The magnitude of induced emf in secondary coil is given by:
$|\epsilon |=M\left|\frac{di}{dt}\right|...\left(i\right)$
where $M=$mutual inductance between primary and secondary coils/windings.
given $\epsilon =40,000\text{V}$ and
$\left|\frac{di}{dt}\right|=\frac{(4-0)\text{A}}{10\times {10}^{-6}\text{s}}=4\times {10}^5\text{A/s}$
From Eq $\left(i\right)$,
$M=\frac{40000}{4\times {10}^5}$
$\therefore M=\frac{1}{10}=0.1\text{H}$