Capacitor Charging

How to Use

• Voltage / Cap / Res sliders — set the source voltage, capacitance, and series resistance.
• Charge — start charging animation; voltage rises exponentially toward Vs.
• Discharge — discharge the capacitor; voltage decays exponentially toward 0.
• Reset — clear charge and graphs instantly.

What to Observe

• Voltage \(V_C\) follows \(V_C(t) = V_s(1 - e^{-t/\tau})\) during charging.
• Current starts high and decays: \(I(t) = \frac{V_s}{R}e^{-t/\tau}\).
• Stored energy \(E = \frac{1}{2}CV_C^2\) grows with the square of voltage.
• After one time constant τ = RC, the capacitor reaches ~63% of its final voltage.
• The three live graphs show V, I, and E simultaneously.

Key Equations

\[\tau = RC\]

\[V_C(t) = V_s\left(1 - e^{-t/\tau}\right) \quad \text{(charging)}\]

\[I(t) = \frac{V_s}{R}e^{-t/\tau}\]

\[E = \frac{1}{2}CV_C^2\]