Question 278: Electromagnetic Induction

Question

Three coils of inductance $$\mathrm{L}_1=2 \mathrm{H}, \mathrm{L}_2=3 \mathrm{H}$$ and $$\mathrm{L}_3=6 \mathrm{H}$$ are connected such that they are separated from each other. To obtain the effective inductance of 1 henry, out of the following combinations as shown in figure, the correct one is

Accepted Answer

The combinations $$\mathrm{P}$$ and $$\mathrm{S}$$ are series combinations. Hence, the effective inductance cannot be $$1 \mathrm{H}$$.
This leaves combinations $$\mathrm{R}$$ and $$\mathrm{Q}$$.
For combination $$\mathrm{R}$$,
$$\mathrm{L}_1+\mathrm{L}_2=5 \mathrm{H}$$
$$\frac{1}{\mathrm{~L}_1+\mathrm{L}_2}+\frac{\mathrm{L}}{\mathrm{L}_3}=\frac{1}{5}+\frac{1}{6}=\frac{6+5}{30}=\frac{11}{30}$$
$$	herefore \quad \mathrm{L}_{	ext {eff }}=\frac{30}{11}=2.72 \mathrm{H}$$
$$	herefore \quad$$ The correct combination would be $$\mathrm{Q}$$.
$$\begin{aligned}
& \quad \frac{1}{\mathrm{~L}_1}+\frac{1}{\mathrm{~L}_2}+\frac{1}{\mathrm{~L}_3}=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}=\frac{3}{6}+\frac{2}{6}+\frac{1}{6} \\
& 	herefore \quad \mathrm{L}_{\mathrm{eff}}=1 \mathrm{H}
\end{aligned}$$

Answer

S

Answer

P

Answer

R

Answer

Q

Electromagnetic Induction

Three coils of inductance $\mathrm{L}_1=2 \mathrm{H}, \mathrm{L}_2=3 \mathrm{H} and \mathrm{L}_3=6 \mathrm{H}$ are connected such that they are separated from each other. To obtain the effective inductance of 1 henry, out of the following combinations as shown in figure, the correct one is

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