MHT CET · Physics · Electromagnetic Induction

Two coils are kept near each other. When no current passess through first coil and current in the \(2^{\text {nd }}\) coil increases at the rate \(10 \mathrm{~A} / \mathrm{s}\), the e.m.f. in the \(1^{\mathbb{x}}\) coil is 20 mV . When no current passes through \(2^{\text {nd }}\) coil and 3.6 A current passes through \(1^8\) coil the flux linkage in coil 2 is

A \(1.2 \times 10^{-3} \mathrm{~Wb}\)
B \(1.8 \times 10^{-3} \mathrm{~Wb}\)
C \(3.6 \times 10^{-3} \mathrm{~Wb}\)
D \(7.2 \times 10^{-3} \mathrm{~Wb}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(7.2 \times 10^{-3} \mathrm{~Wb}\)

Step-by-step Solution

Detailed explanation

The e.m.f. induced in first coil,
\(\begin{aligned}
\therefore \quad \mathrm{e}_1 & =\mathrm{M} \frac{\mathrm{dI}}{\mathrm{dt}} \\
\mathrm{M} & =\frac{\mathrm{e} \times \mathrm{dt}}{\mathrm{dI}_2}...(i)
\end{aligned}\)
Flux linkage of coil, \(\phi=\) MI
\(\begin{aligned}
\phi & =\left(\frac{\mathrm{e} \times \mathrm{dt}}{\mathrm{dI}}\right) \times \mathrm{I}_1 \\
& =\frac{20 \times 10^{-3}}{10} \times 3.6 \\
& =7.2 \times 10^{-3} \mathrm{~Wb}
\end{aligned}\)
. . [From(i)]

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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