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.  

SIMILAR QUESTIONS

Q1

 

The instantaneous current in a circuit is given by I = 2cos (u4t + Ï•) ampere. The r.m.s value of the current is

Q2

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Q3

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Q4

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Q5

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Q6

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Q7

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Q8

A 100-turn rectangular coil of size 0.20 m × 0.10 m rotates in a magnetic field of 0.003 Wb m–2 with a frequency of 1200 rpm about an axis normal to the field. Find the maximum value of the induced emf

Q9

An a.c. generator consists of a coil of 50 turns and area 2.5 m2 rotating at an angular speed of 60 rad s–1 in a uniform magnetic field of 0.30 T. The resistance of the circuit including that of the coil is 500 . Find the maximum current drawn from the generator.    

Q10

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.