A cylindrical conductor has a resistance R. When the conductor is at a temperature `(T)` above its surrounding temperature `(T_0)`, the ratio of therm

Monjur Alahi

A cylindrical conductor has a resistance R. When the conductor is at a temperature `(T)` above its surrounding temperature `(T_0)`, the ratio of thermal power dissipated by the conductor to its excess temperature `(DeltaT = T – T_(0))` above surrounding is a known constant `k`. The conductor is connected to a cell of emf `V`. Initially, the conductor was at room temperature `T_(0)`. Mass and specific heat capacity of the conductor are m and s respectively.
(i) find the time (t) dependence of the temperature (T) of the conductor after it is connected to the cell. Assume no change in resistance due to temperature.
(ii) find the temperature of the conductor after a long time.


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Salim Ahmed Kawsar

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Correct Answer - (i) `T=T_(0)+(V^(2))/(kR)(1-e^(-(kt)/(ms)))`
(ii) `T=T_(0)+(V^(2))/(kR)`

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