The resistance of an electrical toaster has a temperature dependence given by $ R(T)=R_0 [1+α(T−T_0)] $ in its range of operation. At $T_0=300 K, R=100 Ω $and at$ T=500 K, R=120 Ω$. The toaster is connected to a voltage source at $200 V$ and its temperature is raised at a constant rate from $300$ to $ 500 K$ in $30 s$. The total work done in raising the temperature is

Question

$\begin{array}{1 1}(1) 400 \; \ell n \frac{1.5}{1.3} J \\ (2) 200\; \ell n \frac{2}{3} J \\ (3) 400\; \ell n \frac{5}{6} J \\ (4) 60,000 \ell n \frac{6}{5} J \end{array} $