Question

An AC generator consists of a coil of $50$ turns and an area $2.5{\text{m}}^2$ rotating at an angular speed of $60\text{rad/s}$ in a uniform magnetic field of $0.3\text{T}$ between two fixed pole pieces. What is the magnetic flux through the coil, when the current is maximum?

• A. $501\text{Wb}$
• B. $425\text{Wb}$
• C. $334\text{Wb}$
• D. Zero

Answer 1

The correct option is D Zero

The current is maximum, when the coil is horizontal. At this position the magnetic flux through the coil is zero.

$\text{Alternative Solution :}$

Suppose, at any instant, the flux is $\varphi =BA\cos \omega t$

So, induced emf, $E=BA\omega \sin \omega t$

Hence, induced current, $i=\frac{BA\omega }{R}\sin \omega t$

For maximum current, $\omega t=\pi /2$ which gives maximum value of $\sin \omega t=1$.

For $\omega t=\pi /2$, magnetic flux,

$\varphi =BA\cos \omega t=0$