The equivalent inductance of two inductances | vedclass

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(A) Let the two inductances be $L_1$ and $L_2$.For series connection: $L_S = L_1 + L_2 = 10 \, H$ ..... $(i)$For parallel connection: $L_P = \frac{L_1

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$2$

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(A) Let the two inductances be $L_1$ and $L_2$.For series connection: $L_S = L_1 + L_2 = 10 \, H$ ..... $(i)$For parallel connection: $L_P = \frac{L_1 L_2}{L_1 + L_2} = 2.4 \, H$ ..... $(ii)$Substituting $(i)$ into $(ii)$: $L_1 L_2 = 2.4 	imes 10 = 24 \, H^2$ ..... $(iii)$We know the identity: $(L_1 - L_2)^2 = (L_1 + L_2)^2 - 4 L_1 L_2$Substituting the values: $(L_1 - L_2)^2 = (10)^2 - 4(24) = 100 - 96 = 4$Taking the square root: $L_1 - L_2 = \sqrt{4} = 2 \, H$.

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 .......... $H$.

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