A 100 F capacitor is joined to a 24 V battery via a 1.0 M resistor. Which of the following best describes the qualitative graph between charge and time for the first 10 minutes?

Step-by-step solution

The time constant of the RC circuit is given by = RC = (1.0 10^6 )(100 10⁻⁶ F ) = 100 s . The maximum steady-state charge on the capacitor is Q₀ = CV = (100 F )(24 V ) = 2400 C . The equation for the charge on a charging capacitor as a function of time is q(t) = Q₀ (1 - e^ -t/ ) . This equation represents an exponentially growing curve that starts from zero at t = 0 and asymptotically approaches the maximum charge Q₀ = 2400 C . Since the given time interval is 10 minutes = 600 s = 6 , the capacitor will be nearly f