Physics
Capacitor discharge
Calculate voltage, time or time constant during RC discharge.
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Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Initial capacitor voltage. | |
| Voltage after elapsed time t. | |
| Time constant RC in seconds. |
Worked example
- Solve for
- Voltage V
- Initial voltage V₀ (V)
- 5
- Elapsed time t (s)
- 1
- Time constant τ = RC (s)
- 1
1.839397 V
Follow the example steps
- V = V₀e^(−t/τ)
- = 5 × e^(−1/1) = 1.839397 V
Common mistakes
Use the natural logarithm when rearranging an exponential decay.
Incorrect approach
V/V₀ = 0.5: t/τ = −log₁₀(0.5) ≈ 0.3010
Correct approach
t/τ = −ln(0.5) ≈ 0.6931
More checks before you submit
- For discharge, 0 < V ≤ V₀.
- Do not use log base 10 in the exponential law unless you convert the slope appropriately.
- Real leakage, meter resistance and component tolerances can affect the measured curve.
Method notes
Use this for an ideal first-order RC discharge with constant R and C and negligible meter loading.
A plot of ln V against t should be linear with gradient −1/RC when the model is appropriate.