RC Circuit — Capacitor Charging & Discharging
τ = RC • V(t) = V₀(1−e−t/τ) • Charging • Discharging — Simulate • Explore • Practice • Quiz
Understanding RC Circuits — Free Interactive Capacitor Charging & Discharging Simulator
An RC circuit consists of a resistor (R) and a capacitor (C) connected in series with a voltage source. When the switch closes, the capacitor charges through the resistor following an exponential curve: V(t) = V₀(1 − e−t/τ), where τ = RC is the time constant. The time constant represents the time for the voltage to reach 63.2% of its final value. After 5τ, the capacitor is considered fully charged at 99.3% of the supply voltage. Our interactive simulator lets you adjust resistance, capacitance, and supply voltage, then watch the capacitor charge or discharge in real time with animated current dots flowing through the circuit and a live voltage-time graph.
Capacitor Charging & Discharging Curves
During charging, voltage across the capacitor rises exponentially toward the supply voltage while current decreases exponentially from its initial maximum of I₀ = V/R. During discharging, the capacitor releases its stored energy: voltage decays as V(t) = V₀·e−t/τ and current flows in the opposite direction, also decaying exponentially. The simulator displays both curves simultaneously so you can compare charging and discharging behaviour at any resistance and capacitance combination.
Energy Storage and RC Filters
A capacitor stores energy as an electric field between its plates. The energy stored is given by E = ½CV². RC circuits are also fundamental building blocks for electronic filters. A low-pass RC filter passes low-frequency signals while attenuating high frequencies, with a cutoff frequency of fc = 1/(2πRC). A high-pass RC filter does the opposite, blocking DC and passing AC signals above the cutoff frequency. These filters are used extensively in audio electronics, signal processing, and power supply smoothing.
Practical Applications of RC Circuits
RC circuits appear everywhere in electronics: timing circuits in 555 timers, debouncing switches, smoothing rectified power supplies, coupling and decoupling signals between amplifier stages, and setting the bandwidth of communication receivers. The time constant τ = RC is the key design parameter — choosing the right combination of R and C determines how fast the circuit responds. Engineers use RC calculations daily when designing filters, timing delays, and transient response networks.
Who Uses This Simulator?
This simulator is designed for electrical engineering students studying transient analysis, electronics technicians learning about capacitor behaviour, physics students exploring exponential growth and decay, and instructors teaching RC circuit theory. It provides visual, hands-on understanding of time constants, charging curves, and energy storage without requiring laboratory equipment or oscilloscopes.
Explore Related Simulators
If you found this RC Circuit simulator helpful, explore our Ohm’s Law simulator, RLC Circuit simulator, Transformer simulator, and Wheatstone Bridge simulator for more hands-on practice with electrical circuits.