First slide

Inductance

Question

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

Moderate

A

2 henry
B

3 henry
C

4 henry
D

5 henry

Solution

$\begin{array}{l} L_{S} = L_{1} + L_{2} = 10 H . . . . . . . . . . . . . (i) \\ L_{P} = \frac{L_{1} L_{2}}{L_{1} + L_{2}} = 2 .4 H . . . . . . . . . . (ii) \end{array}$
On solving (i) and (ii) L₁L₂ = 24 …....... (iii)
$\begin{array}{l} Also {(L_{1} - L_{2})}^{2} = {(L_{1} + L_{2})}^{2} - 4 L_{1} L_{2} \\ \Rightarrow {(L_{1} - L_{2})}^{2} = (10)^{2} - 4 \times 24 = 4 \Rightarrow L_{1} - L_{2} = 2 H \end{array}$

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