Two concentric circular coils, C1 and C2 are placed in the XY plane… | JEE Main 2020 (5 Sep, Shift 1)

Q53JEE Main 2020 · 5 SEP · SHIFT 1Medium

Mutual Inductance

Two concentric circular coils, C1 and C2 are

placed in the XY plane. C1 has 500 turns, and

a radius of 1 cm. C2 has 200 turns and radius

of 20 cm. C2 carries a time dependent current

I(t) = (5t2 – 2t + 3) A where t is in s. The emf

induced in C1 (in mV), at the instant t = 1 s is

$\frac{4}{x}$ . The value of x is ___.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 5

$M = \frac{\mu_0 N_1 N_2 \pi r_1^2}{2 r_2} = \frac{4\pi\times10^{-7}\times500\times200\times\pi\times10^{-4}}{2\times0.2} = 10\pi^2\times10^{-6}\text{ H}$
$\frac{dI}{dt} = 10t - 2 = 8\text{ A/s}$ at $t = 1\text{ s}$
$e = M\frac{dI}{dt} = 80\pi^2\times10^{-6}\text{ V} \approx 0.8\text{ mV}$ (taking $\pi^2 \approx 10$ )
$\frac{4}{x} = 0.8 \Rightarrow x = 5$

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