How does an RC circuit respond to DC input?

Charging Phase: When a DC voltage is applied to an RC circuit, the capacitor begins to charge. Initially, if the capacitor is uncharged, it acts like a short circuit, and the current flows through the resistor and the capacitor in series.

Exponential Charging: As the capacitor charges up, its voltage increases gradually. The rate of charging follows an exponential curve described by the time constant (ฯ) of the RC circuit, where ฯ = R * C (R is the resistance, and C is the capacitance).

Steady State: In an ideal scenario, the capacitor would fully charge to the DC voltage applied across it. However, in practice, it takes an infinite amount of time to reach the exact value due to the exponential nature of the charging process. In real-world situations, we consider the capacitor fully charged when its voltage is approximately 99% of the DC input voltage.

Blocking Capacitor: Once the capacitor is fully charged, it acts like an open circuit for DC signals. This means that, in the steady state, no current flows through the capacitor, and it effectively blocks the flow of DC through the circuit. The only component allowing current flow is the resistor.

Time Constant: The time constant (ฯ) of the RC circuit determines the charging and discharging behavior. It represents the time it takes for the voltage across the capacitor to reach approximately 63.2% of the final value during charging and to decrease to approximately 36.8% of the initial value during discharging.

In summary, when a DC input is applied to an RC circuit, the capacitor initially allows current to flow, charging up to the input voltage. Once fully charged, the capacitor acts as an open circuit, and no current passes through it. The circuit essentially behaves like a series resistor for DC signals.