Two coils are kept near each other. When no current passess through first coil and current in the $2^{\text…

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
  1. $1.2 \times 10^{-3} \mathrm{~Wb}$
  2. $1.8 \times 10^{-3} \mathrm{~Wb}$
  3. $3.6 \times 10^{-3} \mathrm{~Wb}$
  4. $7.2 \times 10^{-3} \mathrm{~Wb}$

Solution

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)]

Asked in: MHT CET 2024 (03 May Shift 2)

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