A conductor has a temperature independent resistance R and a total heat capacity C. At the moment t = 0 it is connected to a dc voltage V. Find the time dependence of the conductor's temperature T assuming the thermal power dissipated into surrounding space to vary as q = k(T – T 0 ) where k is a constant. T 0 is the environmental temperature (equal to conductor temperature at the initial moment).
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Power 
generated in the resistance is being lost in the environment and utilized in raising the temperature of the conductor.
Hence, 
or C 
= 
– k(T – T 0 )
or 
= 
or 
= 
or T = T 0 + 
(1 – e –kt/C ).
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