Final answer:
In an RLC series circuit, the charge on the capacitor decreases exponentially over time due to the circuit's resistance causing energy dissipation.
Step-by-step explanation:
In the RLC series circuit, when the switch is closed, the capacitor, which is initially fully charged, begins to discharge. The behavior of the charge on the capacitor over time depends on the specific parameters and components in the circuit, such as the resistance (R), inductance (L), and capacitance (C). The electrical oscillations within the circuit are subject to damping due to the resistance, which dissipates energy. Therefore, the charge on the capacitor does not remain constant or increase linearly, instead, it will typically decrease exponentially over time. This behavior can be described by an exponential decay function, indicating that the voltage across the capacitor decreases to 0.368 of its initial value after one-time constant, defined as T = RC.
When examining the behavior of a discharging capacitor, the current initially is driven by the initial voltage Vo on the capacitor. The discharge process is subject to exponential decay, where the charge decreases exponentially as a function of time. The rate of discharge is faster when either the resistance is small (permitting a larger current) or the capacitance is small (storing less charge to begin with). After each time interval equivalent to the time constant (T = RC), the voltage across the capacitor will exponentially approach zero, never quite reaching it but becoming negligibly small after several time constants have passed.
Overall, for an RLC series circuit, the correct answer to the initial question is: A) The charge on the capacitor decreases exponentially.