Q17 of 104 Page 306

Find the total heat produced in the loop of the previous problem during the interval 0 to 30 s if the resistance of the loop is 4.5 mΩ.


Given:


Resistance of the loop R=4.5mΩ


Time interval=30s


As heat produced is a scalar quantity total heat is found by algebraically adding heat produced in different time intervals



Where


heat produced during time interval 0-5s


heat produced during time interval 5-20s


heat produced during time interval 20-25s


heat produced during time interval 25-30s


Now,


(i) during time interval 0-5s emf produced in the loop is given by



Current in the coil is



Heat produced in the coil is given by the formula


…. (i)


where


i=current


R=resistance


t=time interval


putting the values of i, R and t in above eqn. we get,



Emf induced in the time interval 5-20s and 25-30s =0


So current in the coil during this time



Heat produced in the coil is given by eqn.(i)



Emf induced in the time interval 20-25s is same as that induced at 5s



Hence the current and heat produced during this interval is same and given by



Total heat produced is given by





Therefore total heat produced in the loop during interval 0-30s is


More from this chapter

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15

A wire-loop confined in a plane is rotated in its own plane with some angular velocity. A uniform magnetic field exists in the region. Find the emf induced in the loop.

 16

Figure shows a square loop of side 5 cm being moved towards right at a constant speed of 1 cm/s. The front edge enters the 20 cm wide magnetic field at t = 0. Find the emf induced in the loop at

(a) t = 2s, (b) t = 10 s


(c) t = 22 s, (d) t = 30s



 18

A uniform magnetic field B exists in a cylindrical region of radius 10 cm as shown in figure. A uniform wire of length 80 cm and resistance 4.0Ω is bent into a square frame and is placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of 0.010 T/s, find the current induced in the frame.


 19

The magnetic field in the cylindrical region shown in figure increases at a constant rate of 20.0 mT/s. Each side of the square loop abcd and defa has a length of 1.00 cm and a resistance of 4.00 Ω. Find the current (magnitude and since) in the wire ad if

(a) the switch S1 is closed but S2 is open,


(b) S1 is open but S2 is closed,


(c) both S1 and S2 are open and


(d) both S1 and S2 are closed.