Question

The magnetic flux linked with a coil, in webers, is given by the equation: $\varphi =5t^2+3t+16$. The induced e.m.f. in the coil in the fourth second will be

• A. 145 V
• B. 10 V
• C. 210 V
• D. 108 V.

Answer 1

Answer: (B)

Given: Magnetic flux $(\varphi )=5t^2+3t+16.$ We know that the induced e.m.f. $(E)$
$=\frac{d\varphi }{dt}=\frac{d}{dt}\left(5t^2+3t+16\right)=10t+3.$ Therefore induced
e.m.f.; when $t=3,\left(E_3\right)=(10\times 3)+3=33V$
and induced e.m.f. when $t=4,\left(E_4\right)=(10\times 4)+3=43V$.
Therefore e.m.f. induced in the fourth $sec=E_4-E_3$ $=43-33=10V$