In A Dynamo, A Coil Of Area 0.2 M2 and Having 100 Turns Rotates In A Magnetic Field of 0.1 Wb m–2 with An Angular Velocity Of 100 rad s–1. The Output Terminals Are Connected Through A Resistance of . Calculate The torque , As A Function Of Time t, Required To Keep The Coil Rotating.

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Question

In a dynamo, a coil of area 0.2 m2 and having 100 turns rotates in a magnetic field of 0.1 Wb m–2 with an angular velocity of 100 rad s–1. The output terminals are connected through a resistance of . Calculate the torque , as a function of time t, required to keep the coil rotating.

Solution

Correct option is

4 sin 100t

In usual notations, the maximum value of the emf induced in the coil is given by  

           

.  

The maximum current in the circuit is 

           

The instantaneous current in given by 

           .

Let l be the length and b the breadth of the coil (assumed to be rectangular), carrying current i in magnetic field B. The forces experienced by each longer arm, N i B l, from a couple of moment . The torque experienced by the rotating coil is thus given by 

          

               

             .     

An opposite torque of magnitude 4 sin 100t newton-meter is required is keep the coil rotating with uniform angular speed.

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