An a.c. Generator Consisting Of A Coil Of 100 Turns And Cross-sectional Area Of 3 M2 is Rotating At A Constant Angular Speed Of 60 rad s–1 in A Uniform Magnetic Field Of 0.04 T. The Resistance Of The Coil Is 500 . Calculate Maximum Current Drawn From The Generator, And Power Dissipation In The Coil. From Where Does The Power Come? 

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Question

An a.c. generator consisting of a coil of 100 turns and cross-sectional area of 3 m2 is rotating at a constant angular speed of 60 rad s–1 in a uniform magnetic field of 0.04 T. The resistance of the coil is 500 . Calculate maximum current drawn from the generator, and power dissipation in the coil. From where does the power come? 

Solution

Correct option is

518.4 W

The maximum emf induced in the coil is given by  

          .  

               

The maximum current induced in the coil, which can be drawn from the generator is  

          

The power dissipated as heat in the resistance of the coil is  

          

              

                

              = 518.4 W.  

The induced current causes a torque on the coil opposing its rotation (Lenz’s law). An external agent (a rotor) does work to produce a counter torque to make the coil rotate uniformly. This work is the source of power dissipated in the coil.  

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