The equivalent inductance of two inductors is | vedclass

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(B) In series connection,the equivalent inductance is $L_s = L_1 + L_2 = 10 \, H$  ........$(i)$In parallel connection,the equivalent inductance is $L

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$6 \, H, 4 \, H$

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(B) In series connection,the equivalent inductance is $L_s = L_1 + L_2 = 10 \, H$  ........$(i)$In parallel connection,the equivalent inductance is $L_p = \frac{L_1 L_2}{L_1 + L_2} = 2.4 \, H$  ........$(ii)$Substituting the value of $(L_1 + L_2)$ from $(i)$ into $(ii)$,we get:$L_1 L_2 = 2.4 	imes (L_1 + L_2) = 2.4 	imes 10 = 24 \, H^2$Using the identity $(L_1 - L_2)^2 = (L_1 + L_2)^2 - 4 L_1 L_2$,we have:$(L_1 - L_2)^2 = (10)^2 - 4(24) = 100 - 96 = 4$$L_1 - L_2 = \sqrt{4} = 2 \, H$  ........$(iii)$Solving equations $(i)$ and $(iii)$ by adding them:$2 L_1 = 12 \implies L_1 = 6 \, H$Substituting $L_1$ in $(i)$:$6 + L_2 = 10 \implies L_2 = 4 \, H$Thus,the inductances are $6 \, H$ and $4 \, H$.

The equivalent inductance of two inductors is $2.4 \, H$ when connected in parallel and $10 \, H$ when connected in series. What is the value of the inductances of the individual inductors?

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