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Question

Magnetic flux ϕ linked with a stationary loop of resistance R vaires with time t as ϕ=at(Tt). Amount of heat generated in loop during time interval T is

A
aT3R
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B
a2T23R
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C
a2T2R
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D
a2T33R
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Solution

The correct option is A a2T33R
Flux is given by,

X=at(Tt)

emf induced is given by,

e=dXdt

e=2atat

Heat produced during this time perios is given by,

H=T0e2Rdt

H=T04a2t2+a2T24a2TtRdt

H=13R(4a2T3+3a2T36a2T3)

H=a2T33R


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