Question

The magnetic flux linked with a coil, in webers, is given by the equation: $\phi=5 t^{2}+3 t+16$. 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 $(\phi)=5 t^{2}+3 t+16 .$ We know that the induced e.m.f. $(E)$
$=\frac{d \phi}{d t}=\frac{d}{d t}\left(5 t^{2}+3 t+16\right)=10 t+3 .$ Therefore induced
e.m.f.; when $t=3,\left(E_{3}\right)=(10 \times 3)+3=33\, V$
and induced e.m.f. when $t=4,\left(E_{4}\right)=(10 \times 4)+3=43 \,V$.
Therefore e.m.f. induced in the fourth $sec =E_{4}-E_{3}$ $=43-33=10\, V$