Question

The equivalent inductance of two inductors is $2.4 \,H$ when connected in parallel and $10 \,H$ when connected in series. What is the value of inductances of the individual inductors?

• A. $8\,H, \,2\,H$
• B. $6\,H, \,4\,H$
• C. $5\,H, 5\,H$
• D. $7\,H, 3\,H$

Answer 1

Answer: (B)

In series connection $L_{1}+L_{2}=10\,H\dots(i)$
and in parallel connection $\frac{L_{1}L_{2}}{\left(L_{1}+L_{2}\right)}=2.4 \,H \ldots\left(ii\right)$
Substituting the value of $(L_{1}+ L_{2})$ from (i) into (ii), we get
$L_{1}L_{2}=\left(2.4\right)\left(L_{1}+L_{2}\right)=2.4\times10=24$
$\left(L_{1}-L_{2}\right)^{2}=\left(L_{1}+L_{2}\right)^{2}-4L_{1}L_{2}$
$L_{1}-L_{2}=\left[\left(10\right)^{2}-4\times24\right]^{1 2}=2H\ldots\left(iii\right)$
Solving $\left(i\right)$ and $\left(iii\right)$, we get
$L_{1}=6\,H, L_{2}=4\,H$