Library / Foundations: Physics / FPH-25
Foundations: Physics
Capacitor discharge
Charge remaining after a capacitor discharges through a resistor.
- Ref
- FPH-25
- Rev
- v1
- Field
- Foundations: Physics
- Result
- Q [µC]
During discharge through R, Q = Q₀ exp[−t/(RC)] and the time constant RC is in seconds.
A discharging capacitor loses charge by the same fraction in each equal time, so it falls steeply at first and then slowly.
Calculator
- Time constant RC2 s
- Fraction remaining36.79 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- After one time constant, 36.8% of the charge remains; after 5 time constants less than 1%.
- Voltage and current fall in the same exponential way as charge.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (µC) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Q₀ Initial charge | 1 to 100,000 µC | 0.3679 | 36,790 | 36,790 | +10% | +10 % |
| C Capacitance | 1 to 10,000 µF | 3.72e-41 | 990 | 990 | +10% | +9.52 % |
| R Resistance | 1 to 1,000 kΩ | 2.061e-6 | 980.2 | 980.2 | +10% | +9.52 % |
| t Time | 0.1 to 20 s | 0.0454 | 951.2 | 951.2 | +10% | −9.52 % |
Sweep of Time
| Time (s) | Charge remaining (µC) |
|---|---|
| 0.1 | 951.2 |
| 0.1939 | 907.6 |
| 0.3761 | 828.6 |
| 0.7293 | 694.5 |
| 1.414 | 493.1 |
| 2.742 | 253.8 |
| 5.318 | 70.01 |
| 10.31 | 5.761 |
| 20 | 0.0454 |
Sweep one variable
Variables and how each one contributes
Charge remaining
What the equation gives you. Everything else feeds it.
Initial charge
Charge at t = 0. Directly proportional.
Resistance
Resistance in the discharge path. Slows the discharge.
Capacitance
Capacitance. Slows the discharge.
Time
Elapsed time. Exponential decay.
Worked example with the values above
- Time constant: RC = 20 kΩ × 100 µF = 2 s.
- Exponent: t/RC = 1; e−x = 0.3679.
- Q = 367.9 µC.
Assumptions and limits
- Ideal components.
- Discharge through a fixed resistor.
Common mistakes
- Using ms and s inconsistently.
- Treating the decay as linear.
Statistics and uncertainty
Component tolerances can make RC off by 20% or more, which shifts the whole curve; measure the time constant in the circuit if timing matters.
Where it is used
- Timing and delay circuits.
- Safe discharge of capacitors.
Maths you need
- Exponentials: e^(−x)
- Time constant: τ = RC