Question

If the resistance of conductor is $R$, then total heat dissipated across resistance $R$ is:

• A. $\frac{i_0^{2}R{t}_0}{2}$
• B. $\frac{i_0^{2}R{t}_0}{4}$
• C. $\frac{i_0^{2}R{t}_0}{3}$
• D. $i_0^{2}R{t}_0$

Answer 1

The correct option is C $\frac{i_0^{2}R{t}_0}{3}$

Equation = $\frac{i}{i_0}+\frac{t}{t_0}=1$

Heat dissipated $=\int c^2{R}_{dt}={\int }_0^{to}{\left(\frac{-t}{t_0}\right)}^2{i}_0^2{R}_{at}$

On solving integration we get ,

Heat dissipated $=\frac{i_0^{2}R{t}_0}{3}$ Joules