Q. The equivalent inductance of two inductance is $2.4\ henry$ when connected in parallel and $10\ henry$ when connected in series. The difference between the two inductances is
A) $2\ henry$
B) $3\ henry$
C) $4\ henry$
D) $5\ henry$
Explanation
(a) $L_{S} = L_{1} + L_{2} = 10H$ …(i)
$L_{P} = \frac{L_{1}L_{2}}{L_{1} + L_{2}} = 2.4H$ …(ii)
On solving (i) and (ii) $L_{1}L_{2} = 24$ …(iii)
Also $\left( L_{1} - L_{2} \right)^{2} = \left( L_{1} + L_{2} \right)^{2} - 4L_{2}L_{2}$
$\Rightarrow \left( L_{1} - L_{2} \right)^{2} = (10)^{2} - 4 \times 24 = 4 \Rightarrow L_{1} - L_{2} = 2H$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.