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A resistor has initial resistance 'R 0 ' at 0 º C. Now, it is connected to an ideal battery of constant emf = 'v'. If the temperature co–efficient of resistance is α, then after how much time, will its temperature be 'T º C' (mass of the wire = m, specific heat capacity of the wire = S). Assume the resistance varies linearly with temperature neglect heat loss to the surrounding.

A resistor has initial resistance 'R0' at 0ºC. Now, it is connected to an ideal battery of constant emf = 'v'. If the temperature co–efficient of resistance is α, then after how much time, will its temperature be 'TºC' (mass of  the wire = m, specific heat capacity of the wire = S). Assume the resistance varies linearly with temperature neglect heat loss to the surrounding.

Grade:12

1 Answers

Shobhit Varshney IIT Roorkee
askIITians Faculty 33 Points
7 years ago
Dear student,

Resistance here is time dependent, so heat energy per unit time (power) will also be a function of time. So, we need to consider dt time interval, which will increase the temperature by dT. Use integration to find out the time required for T temp increase.

Thanks.

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