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A conductor has a temperature independen...

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 times dependence of the conductors 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 surrounding temperature (equal to conductor's temperature at the initial moment).

A

`T=(V^(2))/(kR)e^((-kt)/(C ))`

B

`T=T_(0)+(V^(2))/(KR)[1-e^((-Kt)/(C ))]`

C

`T=T_(0)+(V^(2))/(kR)e^((-kt)/(C ))`

D

`T=(T_(0)+(V^(2))/(kR))e^((-kt)/(C ))`

Text Solution

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The correct Answer is:
B
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