How does a capacitor behave in a DC circuit over time?

• A. It becomes a short circuit after a long time.
• B. It charges toward the supply voltage; current decays to zero; in steady state acts as an open circuit.
• C. It continuously charges and discharges with the same current.
• D. It blocks DC indefinitely.

Answer: (B)

In a DC circuit, a capacitor responds by charging up toward the supply voltage. At first, current flows as the capacitor accumulates charge, but as the voltage across it rises, the driving force for current diminishes and the current decays toward zero. When the capacitor is fully charged, dv/dt is essentially zero, so no further current flows and the capacitor acts like an open circuit in the steady state. If a resistor is in the circuit, the charging follows an exponential curve with a time constant determined by the resistance and the capacitance, but the end behavior remains that the current stops and the capacitor voltage reaches the supply.