Final answer:
The absolute value of the rate of change of stored energy in a discharging capacitor depends on time. The charge on the capacitor can be expressed as q(t) = Qe^(-t/T) and the time rate of change of energy as dE/dt = -Q/T * V * e^(-t/T).
Step-by-step explanation:
The absolute value of the rate of change of stored energy in a discharging capacitor depends on time. As the capacitor discharges, the amount of stored energy decreases. The rate at which the energy decreases is given by the time derivative of the charge on the capacitor.
The charge on the capacitor can be expressed as q(t) = Qe^(-t/T), where Q is the initial charge on the capacitor and T = RC is the time constant of the circuit. Taking the time derivative of this equation gives us dq/dt = -Q/T * e^(-t/T).
Since energy stored in a capacitor is related to the charge Q and the voltage V, we can express the rate of change of energy as dE/dt = V(dq/dt), where V = Q/C is the voltage across the capacitor. Therefore, the expression for the time rate of change of energy inside the capacitor is dE/dt = -Q/T * V * e^(-t/T).