Question

# The relation between current in a conductor and time is shown in the figure. (iii) If the resistance of the conductor is R then the total heat dissipated across resistance R is ​​​​​​​[1 Mark]

A
i20Rt02
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B
i20Rt04
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C
i20Rt03
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D
i20Rt0
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Solution

## The correct option is C i20Rt03Let dH be the small amount of heat dissipated in time dt i.e dH=i2R dt Total heat dissipated ∫H0dH=∫t00i2R dt The expression for i in terms of t is given by i=i0(1−tt0) H=∫t00i20(1−tt0)2R dt H=i20R∫t00(1−tt0)2dt ∴H=i20R⎡⎢ ⎢ ⎢ ⎢ ⎢⎣(1−tt0)33(−1t0)⎤⎥ ⎥ ⎥ ⎥ ⎥⎦t00 H=i20Rt03 So, option (c) is correct.

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