Capacitor Charge/Discharge

Interactive simulation demonstrating RC circuit behavior during capacitor charging and discharging

Circuit Visualization

Voltage: 0.00 V
Charge: 0.00 μC
Current: 0.00 mA
Time Constant (τ): 1.00 s
Time: 0.00 s

Circuit Parameters

Component Values

Animation Controls

Display Options

RC Circuit Equations

Charging: q(t) = Q₀(1 - e^(-t/RC))
Discharging: q(t) = Q₀·e^(-t/RC)
Time Constant: τ = RC
Voltage: V = q/C
Charging Current: I = (V₀/R)·e^(-t/RC)
Discharging Current: I = -(Q₀/RC)·e^(-t/RC)
Current Parameters: τ = 1.00 s, Q₀ = 100.00 μC, I₀ = 0.10 mA

Instructions

  • Click "Charge" to connect the capacitor to the voltage source
  • Click "Discharge" to disconnect the source and discharge through the resistor
  • Observe how voltage and current change exponentially with time
  • The time constant τ = RC determines the charging/discharging speed
  • After 5τ, the capacitor is 99.3% charged or discharged
  • Switch between circuit diagram, curves, and comparison views

What is Capacitor Charge/Discharge?

A capacitor is an electrical component that stores energy in an electric field. When connected to a voltage source through a resistor, it charges exponentially as charge accumulates on its plates. The voltage across the capacitor increases until it equals the source voltage. When disconnected from the source and connected to a discharge path, the stored charge flows out, causing the voltage to decay exponentially.

Charging Process

During charging, the charge on the capacitor follows q(t) = Q₀(1 - e^(-t/RC)), where Q₀ = CV₀ is the maximum charge. Initially, the capacitor acts like a short circuit, and maximum current I₀ = V₀/R flows. As charge accumulates, the voltage across the capacitor opposes the source voltage, reducing the current. After one time constant τ = RC, the capacitor reaches 63.2% of its final charge. After 5τ, it's effectively fully charged (99.3%).

Discharging Process

During discharging, the capacitor acts as the voltage source. The charge follows q(t) = Q₀·e^(-t/RC), starting from its initial charge Q₀ and decaying to zero. The current flows in the opposite direction during discharge. The voltage across the capacitor decreases as V(t) = V₀·e^(-t/RC). The discharge follows the same exponential time constant τ = RC, with 63.2% of the charge gone after one time constant.

Time Constant

The time constant τ = RC is the characteristic time scale of the circuit. A larger τ means slower charging/discharging. At t = τ, the capacitor has reached 63.2% of its final value during charging, or lost 63.2% of its initial charge during discharging. At t = 5τ, the process is 99.3% complete, considered fully charged or discharged for most practical purposes. The product RC has units of seconds when R is in ohms and C is in farads.

Energy Storage

A charged capacitor stores energy in its electric field, given by E = ½CV² = q²/(2C). This energy is supplied by the voltage source during charging (half stored in the capacitor, half dissipated in the resistor). During discharging, this stored energy is released, primarily as heat in the resistor. This energy storage property makes capacitors useful in flash photography, defibrillators, power supplies, and many other applications.

Applications

RC circuits with capacitors have numerous applications: timing circuits and delays in electronics; filters in audio and radio systems; power supply smoothing; camera flash units; defibrillators; energy storage in regenerative braking; touchscreens and touch sensors; coupling and decoupling in amplifiers; sample-and-hold circuits; and as memory elements in early computers. The exponential charging/discharging behavior is fundamental to understanding transient analysis in electrical circuits.