RC Circuit — Capacitor Charging & Discharging

The RC Circuit Simulator lets you explore how a resistor-capacitor circuit behaves during charging and discharging. The core relationship is the time constant τ = RC, which determines how quickly a capacitor charges or discharges through a resistor. During charging, the capacitor voltage follows V(t) = V₀(1 − e^−t/τ), reaching 63.2% of the supply voltage after one time constant and 99.3% after five time constants (5τ).

This simulator is built for electrical engineering students, electronics technicians, and physics learners studying transient analysis, exponential decay, cutoff frequency, and RC filter design. You can adjust resistance, capacitance, and supply voltage, then watch the capacitor charge or discharge in real time with animated current flow and a live voltage-time graph.

The simulator opens in Simulate mode with R = 1000 Ω, C = 100 μF, and V_supply = 12 V, giving a time constant of τ = 0.1 s. To begin:

• Click Charge or Discharge to select the operating mode, then observe the voltage curve on the canvas.
• Drag the R slider (1–10,000 Ω) and C slider (1–1000 μF) to change the time constant and see the curve stretch or compress.
• Adjust the V_supply slider (1–24 V) to change the final voltage the capacitor charges toward.
• Use Presets to load common RC combinations: Fast (10 Ω, 100 μF), Standard (1 kΩ, 100 μF), Slow (10 kΩ, 1000 μF), or Filter (1 kΩ, 10 μF).
• Click Reset to restart the animation from t = 0.

Switch between the four modes — Simulate, Explore, Practice, Quiz — using the pill tabs at the top of the page.

Simulate mode is the primary interactive workspace. The canvas displays the RC circuit schematic with animated current dots and a real-time voltage-vs-time graph. Key controls include:

• R slider (1–10,000 Ω): Controls resistance. Higher R means a longer time constant and slower charging.
• C slider (1–1000 μF): Controls capacitance. Higher C stores more charge and takes longer to reach full voltage.
• V_supply slider (1–24 V): Sets the target voltage for charging. During discharge, the capacitor starts at this voltage.
• Charge / Discharge toggle: Switches between charging (voltage rises exponentially) and discharging (voltage decays exponentially as V(t) = V₀·e^−t/τ).

The readout cards show: capacitor voltage (V_C), time constant (τ), instantaneous current, energy stored (E = ½CV²), and charge percentage. Watch how the current starts at maximum (I₀ = V/R) and decays exponentially as the capacitor charges.

Explore mode organises educational content into three categories:

• Fundamentals: Covers capacitor construction, capacitance definition (C = Q/V), electric field between plates, and the relationship between charge, voltage, and energy storage.
• Time Response: Explains the exponential charging and discharging curves, the meaning of τ = RC, the 5τ rule for full charge, and how to read time-domain waveforms.
• Applications: Describes real-world uses of RC circuits including low-pass and high-pass filters (cutoff frequency f_c = 1/(2πRC)), timing circuits, switch debouncing, and power supply smoothing.

Select any concept card to view a detailed explanation with formulas and an interactive canvas illustration.

Practice mode generates unlimited calculation problems on RC circuits. Typical questions include: “Calculate the time constant for R = 2.2 kΩ and C = 47 μF”, “What is the capacitor voltage after 3τ when charging from 0 to 12 V?”, or “Find the cutoff frequency of an RC filter with R = 1 kΩ and C = 10 μF.” Enter your numeric answer, click Check, and see a step-by-step solution.

Quiz mode presents 5 multiple-choice questions covering time constant calculations, exponential decay, energy storage, and filter behaviour. Your score is shown at the end with explanations for each answer.

• Remember the 5τ rule: after 5 time constants, the capacitor is at 99.3% of its final value — effectively fully charged or discharged.
• Compare charging and discharging curves side by side by switching modes and clicking Reset each time.
• Use the Fast preset (10 Ω, 100 μF) to see rapid charging, then switch to Slow (10 kΩ, 1000 μF) to observe a much longer time constant.
• Watch the current readout during charging — it starts at I₀ = V/R and decays to near zero, confirming exponential behaviour.
• For filter design, remember that f_c = 1/(2πRC). A larger RC product gives a lower cutoff frequency.
• The energy stored in the capacitor (E = ½CV²) increases quadratically with voltage, so doubling voltage quadruples energy.
• Practice converting between time constant notation and actual seconds: τ = RC in seconds when R is in ohms and C is in farads.