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Sinusoidal AC

An A.C. gener...

Question

An A.C. generator consists of a coil of 100 turns arid cross-sectional area of 3 $m^{2}$ , rotating at a constant angular speed of 60 radian/sec in a uniform magnetic field of 0.4 T. The resistance of the coil is 500 ohm. What is the maximum power dissipation in the coil?

518.4 W

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1296W

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259.2W

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Zero

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Solution

The correct option is A 1296W
$N = 100, A = 3 m^{2}, ω = 60 r a d / s$
$B = 0.4 T R = 500 Ω$
As induced emf is given by $= N B A ω s i n ω t$
Max emf $e_{0} = N B A ω = 100 \times 0.4 \times 3 \times 60$
$= 7200$ Volt
Induced current ( max ) $I_{0} = \frac{e_{o}}{R} = 7200 / 500 = 18 A$

Power $= e_{0} I_{0}$ $7200 \times 18 = 1.296 \times 10^{3} w a t t$

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