Find an expression for the voltage across the capacitor in...

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Key Concepts

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law is fundamental in circuit analysis and states that the sum of all voltages around any closed loop in a circuit must equal zero. By applying KVL to an RC circuit, one can determine the voltage across the capacitor by accounting for the voltage drops across other components, thereby confirming that when the capacitor is fully charged, its voltage equals the supply voltage.

Steady-State Behavior in DC Circuits

When an RC circuit reaches steady state, all transient behavior has subsided and the voltage across the capacitor no longer changes. In this fully charged condition, the capacitor acts like an open circuit. This means that the capacitor’s voltage equals the applied DC supply voltage, as no current flows through the circuit.

Capacitor Charging in RC Circuits

In resistor-capacitor (RC) circuits, a capacitor charges over time when connected to a voltage supply. As the capacitor accumulates charge, the voltage across its plates increases exponentially until it eventually reaches the supply voltage. The time constant of the circuit, given by the product of resistance and capacitance (RC), determines how quickly the capacitor charges.

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