Question

Two inductances connected in parallel are equivalent to a single inductance of $1.5 H$ and when connected in series are equivalent to a single inductance of $8 H$. The difference in their inductance is:

• A. $3 H$
• B. $7.5 H$
• C. $2 H$
• D. $4 H$

Answer 1

Answer: (D)

$\therefore $ In parallel, $L_{p}=\frac{L_{1} L_{2}}{L_{1}+L_{2}}$
$\left( L _{1}+ L _{2}\right) 1.5= L _{1} L _{2}$
and in series, $L_{S}=L_{1}+L_{2}=8$
$\therefore L _{1} L _{2}=12$
$\left(L_{1}-L_{2}\right)^{2}=\left(L_{1}+L_{2}\right)^{2}-4 L_{1} L_{2}$
$L _{ D }=\sqrt{(6)^{2}-4 \times 12}$
$L _{ D }=4 H$