Question

Two inductors whose self-inductances are of $20\text{mH}$ and $30\text{mH}$ respectively are connected together in parallel opposing. Their mutual inductance is given as $5\text{mH}$. Calculate the total inductance of the parallel combination.

• A. $3.6\text{mH}$
• B. $5.6\text{mH}$
• C. $7.6\text{mH}$
• D. $9.6\text{mH}$

Answer 1

The correct option is D $9.6\text{mH}$

We know that, for a parallel combination of inductors such that their magnetic fields oppose each other, net inductance is given by,

$L_{eq}=\frac{L_1{L}_2-M^2}{L_1+L_2+2M}$

$\Rightarrow L_{eq}=\frac{20\times 30-5^2}{20+30+2\times 5}$

$\Rightarrow L_{eq}=9.6\text{mH}$