RC Circuits: Discharging A Capacitor

When the battery disconnects, the capacitor discharges through the resistor. The charge decreases exponentially from its initial maximum value toward zero. The circuit reduces to a simple series connection of the resistor, capacitor, and switch, with the voltage source completely removed from the circuit.

The discharge current decays exponentially with time, starting at its maximum value and approaching zero as time increases. The negative sign in the current expression indicates the current flows opposite to the charging direction. The current magnitude decreases continuously throughout the discharge process.

The negative sign signifies that the current direction during discharge is opposite to the current direction during charging. Since the capacitor loses charge with time, the negative sign reflects this opposite flow direction compared to when the capacitor was acquiring charge from the voltage source.

The charge on a discharging capacitor decreases exponentially as a function of time, starting from the maximum charge acquired during charging. Using Kirchhoff's loop rule and integrating the resulting equation yields this exponential decay relationship, where charge approaches zero as time approaches infinity.

A relaxation oscillator comprises a voltage source, capacitor, resistor, and neon lamp. The lamp acts as an open circuit until voltage reaches a threshold, then acts as a short circuit, allowing the capacitor to discharge through it and produce light. The process repeats as the capacitor recharges, creating flashing controlled by R and C values.

Both voltage and charge magnitudes decrease exponentially during discharge, approaching zero as time increases. Since voltage across the capacitor is proportional to the charge stored, they decay together at the same exponential rate determined by the RC time constant of the circuit.

During charging, a voltage source drives charge onto the capacitor; during discharge, no external source exists and the capacitor releases stored charge through the resistor. The current direction reverses, indicated by the negative sign in the discharge current equation, though both processes follow exponential behavior.