Question

In a region of uniform magnetic induction $B={10}^{-2}tesla$, a circular coil of radius 30 cm and resistance ${\pi }^2$ ohm is rotated about an axis, which is perpendicular to the direction of B and which forms a diameter of coil. If the coil rotates at 200 r.p.m., the amplitude of alternating current induced in the coil is :-

• A. $4{\pi }^2$ mA
• B. 30 mA
• C. 6 mA
• D. 200 mA

Answer 1

The correct option is C 6 mA

$\begin{array}{c}{I}_o=\frac{E_o}{R}=\frac{nBAw}{R}\\ Given,n=1,B={10}^{-2}T\\ A=p{\left(0.3\right)}^2{m}^2,R=p^2\\ f=\left(\frac{200}{60}\right)andw=2\pi \left(\frac{200}{60}\right)\\ substituingthesevaluesandsolving,weget\\ I=6\times {10}^{-3}A=6mA\end{array}$

Hence,

option $\left(C\right)$ is correct answer.