The number of turns in the coil of an ac generator is 5000 and the area of the coil is 0.25 m². The coil is rotated at the rate of 100 cycles/sec in a magnetic field of 0.2 T. The peak value of the emf generated is nearly 
 

Given data: $\text{ AC generator is }5000\text{. }$Area of the coil is $0.25 {\text{m}}^2$.

Concept used: Alternating current 

Detailed solution:

$$\begin{gathered} \mathrm{magnetic} \mathrm{flux} \mathrm{linked} \mathrm{with} \mathrm{the} \mathrm{coil} \\ \mathrm{\varphi }=\mathrm{NABcos\omega t} \end{gathered}$$

$$\begin{gathered} \mathrm{induced} \mathrm{emf} \mathrm{e}=-\frac{\mathrm{d\varphi }}{\mathrm{dt}}=\mathrm{NAB\omega sin\omega t} \\ \mathrm{Maximum} \mathrm{emf}=\mathrm{NAB\omega } \end{gathered}$$

$$\begin{gathered} e_0=2\times 3.14\times 100\times 5000\times 0.2\times 0.25 \\ {e}_0=157\text{kV} \end{gathered}$$