Question

An armature coil consists of $20$ turns of wire each of area $0.09{\text{m}}^2$ and resistance $15\Omega$. It rotates in a magnetic field of $0.5\text{T}$ at a constant frequency of $\frac{150}{11}\text{Hz}$. Find the average induced emf produced in the coil in one complete cycle.

• A. $270\text{V}$
• B. $135\text{V}$
• C. $0\text{V}$
• D. None of the above

Answer 1

The correct option is C $0\text{V}$

For a loop having $N$ turns, the total induced emf across the two ends of the loop is,

$E=-N\frac{d\varphi }{dt}=-N\frac{d}{dt}\left(BA\cos \omega t\right)$

$\therefore E=NBA\omega \sin \omega t$

For average induced emf $\left(E\right)$, we have to integrate induced emf with respect to the given time interval.

Here, given time period, $t=T\left(\text{one complete period}\right)$

The average emf or current in this case will be zero.



Note: The average value of $\sin$ and $\cos$ function in one complete time period is always zero.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(\text{C}\right)$ is the correct answer.