Set R and C, choose Charge or Discharge, then press Start. Click Capture at any moment to record V_C, I, Q, and % charged. Vary τ = RC to see how the curve changes speed.
Recorded Data
Mode
t (s)
V_C (V)
I (mA)
Q (mC)
U (µJ)
P_R (mW)
Start sim then click Capture
V_C vs t/tau
Record 2+ points to see graph
What To Explore
Double R — does the time constant double? Verify τ = RC.
At t = 1τ the capacitor is 63.2% charged. Record V_C and check against V₀ × 0.632.
Switch to Discharge. Capture V_C at 1τ — it should be 36.8% of V₀ (= 1/e).
EQUATION LAB — RC Circuit Charging & Discharging
Symbols
V₀Supply voltage (Volts)
V_CVoltage across capacitor (V)
RResistance (Ohms)
CCapacitance (Farads)
τTime constant = RC (seconds)
QCharge on capacitor = CV_C (Coulombs)
ICurrent = dQ/dt (Amperes)
Laws
Time Constant
After 1τ: 63.2% charged. After 5τ: 99.3% — considered fully charged. Larger R or C → slower response.
Charging Equation
From KVL: V₀ = IR + V_C. With I = C·dV_C/dt this gives the ODE whose solution is the exponential rise.
Discharging Equation
No source in loop: 0 = IR + V_C. The stored energy dissipates exponentially through R.
Current & Charge
Current magnitude decays as (V₀/R)e^{−t/τ}. Discharge current flows in reverse (−ve sign). Q = CV_C tracks the charge stored.
Energy & Power
U_C is electrostatic energy stored in the electric field between the plates. P_R is Joule heating in R — equal to rate of energy lost by capacitor during discharge.