Answer
The rate at which thermal energy is produced in the resistor is $~~(e^{-2t})~Watts$
Work Step by Step
In part (d), we found that $~~V_R = 1000~e^{-t}$
We can find the rate at which thermal energy is produced in the resistor:
$P = \frac{V_R^2}{R}$
$P = \frac{(1000~e^{-t})^2}{1.0\times 10^6~\Omega}$
$P = (e^{-2t})~Watts$
The rate at which thermal energy is produced in the resistor is $~~(e^{-2t})~Watts$
