Question 91: AC fundamentals

Question

A square shaped coil of area $$70 \mathrm{~cm}^{2}$$ having 600 turns rotates in a magnetic field of $$0.4 ~\mathrm{wbm}^{-2}$$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $$60^{\circ}$$ with the field, will be ____________ V. (Take $$\pi=\frac{22}{7}$$)

Accepted Answer

Area $(\mathrm{A})=70 \mathrm{~cm}^2=70 	imes 10^{-4} \mathrm{~m}^2$
$$
\mathrm{B}=0.4 \mathrm{~T}
$$
$f=\frac{500 	ext { revolution }}{60 	ext { minute }}=\frac{500}{60} \frac{	ext { rev. }}{\mathrm{sec} .}$
Induced emf in rotating coil is given by
$$
\begin{aligned}
& e=N \omega B A \sin 	heta \\
& =600 	imes 2 	imes \frac{22}{7} 	imes \frac{500}{60} 	imes 0.4 	imes 70 	imes 10^{-4} \sin 30^{\circ} \\
& =600 	imes 2 	imes \frac{22}{7} 	imes \frac{500}{6} 	imes 0.4 	imes 70 	imes 10^{-4} 	imes \frac{1}{2} \\
& =44 	ext { Volt }
\end{aligned}
$$

AC fundamentals

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