This tool calculates the time it takes to discharge a capacitor (in a Resistor Capacitor network) to a specified voltage level. It’s also called RC discharge time calculator.
To calculate the time it takes to discharge a capacitor is to enter:
- Final Voltage (V)
- Initial Voltage (Vo)
- Resistance (R)
- Capacitance (C)
Formula
V = Vo*e−t/RC
t = RC*Loge(Vo/V)
The time constant Ï„ = RC, where R is resistance and C is capacitance. The time t is typically specified as a multiple of the time constant.
Example Calculation
Example 1
Use values for Resistance, R = 10 Ω and Capacitance, C = 1 µF.
For an initial voltage of 10V and final voltage of 1V the time it takes to discharge to this level is 23 µs.
For the same RC values the time it takes to get to a ratio of 1/100 or 0.01 is 46 µs.
Example 2
Find the time to discharge a 470 µF capacitor from 240 Volt to 60 Volt with 33 kΩ discharge resistor.
Using these values in the above two calculators, the answer is 21.5 seconds.
Use this calculator to find the required resistance when the discharge time and capacitance is specified
Background
Capacitor discharge time refers to the period it takes for a capacitor to release its stored energy and decrease its voltage from an initial level (V) to a specific lower level (Vo), typically to either a negligible voltage or to a fraction of the initial voltage. This discharge process is important in various electronic circuits, including timing circuits, filters, and power supply systems.
The discharge time of a capacitor is primarily governed by the RC time constant (often denoted as Ï„), where R is the resistance through which the capacitor discharges, and C is the capacitance.
The time constant represents the time required for the voltage across the capacitor to decrease to about 36.8% (substitute t=RC in the equation e−t/RC . This gives e-1 = 1/e, where e is the base of the natural logarithm) of its initial value during the discharge process.
Frequently Asked Questions
How fast does a capacitor discharge?
The speed at which a capacitor discharges depends on its capacitance and the resistor it is connected to. It depends on the RC time constant.
In general, a capacitor is considered fully charged when it reaches 99.33% of the input voltage. Conversely a cap is fully discharged when it loses the same amount of charge. The amount of charge remaining on the cap in this case is 0.67%.
The ratio Vo/V = 0.67/100 = 0.0067 can be used in the calculator above. For a 470 µF capacitor and 33 kΩ it takes 77.64 seconds. This is approximately the same as 5*RC (or five time constants).
The lower the RC time constant the quicker the discharge.
This time constant is the reason that an LED light on your TV or any electronic equipment will stay on even after you turn it off. It’s also why you should be careful when opening up electronics – the capacitors can carry a significant voltage.
Why do we use five time constants?
In a related post we explained why it takes 5 time constants to charge a capacitor. The reasoning is similar for capacitor discharging. The table below shows the multiple of time constant vs. % charge.
| Number of time constants | % charge |
|---|---|
| 0 | 100.0000000000 |
| 0.5 | 60.6530659713 |
| 1 | 36.7879441171 |
| 2 | 13.5335283237 |
| 3 | 4.9787068368 |
| 4 | 1.8315638889 |
| 5 | 0.6737946999 |
| 6 | 0.2478752177 |
| 7 | 0.0911881966 |
| 8 | 0.0335462628 |
| 9 | 0.0123409804 |
| 10 | 0.0045399930 |
At time t=0, the capacitor is fully charged (100%). As time progresses, the charge decreases exponentially. At 5 time constants the amount of charge remaining is less than 1%.
Other Calculators
- Capacitor Reactance
- Equivalent Series Resistance (ESR)
- Cap power dissipation
- Capacitor discharge and peak current
- Log with any base
- Super capacitor discharge time calculator for both resistor load and constant current