In a capacitor-charging circuit, let Q₁ denote the charge delivered to the capacitor during an initial time interval of 10 ms , and let Q₂ denote the charge delivered during the subsequent 10 ms interval. Additionally, assume that an initial 10 C of charge is deposited over a time interval t₁ , while the next 10 C of charge is deposited over the following time interval t₂ .

Step-by-step solution

The charge on a capacitor during charging is given by q(t) = Q₀(1 - e^ -t/RC ) . The charging current is the rate of flow of charge, given by i(t) = dq dt = Q₀ RC e^ -t/RC . Since the current i(t) decreases exponentially with time, the rate at which charge is delivered to the capacitor continuously decreases. For a fixed time interval, the charge delivered is the area under the i(t) curve. Because i(t) is a decreasing function, the charge delivered in the first 10 ms interval is greater than the charge delivered in