First slide

Inductance

Question

The equivalent inductance of two inductances is 2.4 H when connected in parallel and 10 H when connected in series. The difference between the two inductances is

Moderate

A

2 H
B

3 H
C

4 H
D

5 H

Solution

$L_{s} = L_{1} + L_{2} = 10 H$ …(i)
$L_{p} = \frac{L_{1} L_{2}}{L_{1} + L_{2}} = 2.4 H$ …(ii)
On solving (i) and (ii), $L_{1} L_{2} = 24$ …(iii)
Also ${(L_{1} - L_{2})}^{2} = {(L_{1} + L_{2})}^{2} - 4 L_{1} L_{2}$
$\Rightarrow {(L_{1} - L_{2})}^{2} = (10)^{2} - 4 \times 24 = 4 \Rightarrow L_{1} - L_{2} = 2 H$

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