# Calculate Time for Discharging Capacitors

• Rupturez
In summary, the conversation discusses the equation for instantaneous voltage of a discharging capacitor and the difficulty in finding the precise time for the capacitor to completely discharge to zero volts. Suggestions are given to determine a practical time for the capacitor to reach a desired voltage, such as 5% or 1% of the initial voltage, which would take approximately 3 or 5 time constants respectively.
Rupturez
Hi there,
okay my Question is on discharging capacitors.
the equation for instantanious voltage of a capacitor whilst dischargeing is : v=Vi*e^-t/R*C

However I am not sure how to find the time for a capacitor to completely discharge to zero volts.

When I transpose for t
t=-(R*C)*ln(v/Vi)

and input v as zero (cap has completely discharge) we get an undefined answear.
I havnt studied calculus and am not familiar with the concept of limits.

how would I go about finding the precise time for a capacitor to discharge without using a normalised universal time constant curve to estimate the answear.

Of course you get a dippy answer. With exponential processes, you Never get to zero. Each interval of RC seconds, the volts decrease by 1/e. You can't get to zero without an infinite value for the time.
Of course, 'as near zero as dammit' would take a very finite time! (Engineer speaking)

I understand the voltage will never actually reach absolute zero, however I am after the "practicle" time for the capacitor to reach "practicle" zero voltage.

First decide on what is an acceptably low voltage for your purpose and then put it in your formula.

Rupturez said:
I understand the voltage will never actually reach absolute zero, however I am after the "practicle" time for the capacitor to reach "practicle" zero voltage.

Hi Ruptures. As sophiecentaur has pointed out, it is the nature of the (negative) exponential function that it never reaches precisely zero in any finite time. A "practical" time depends upon just how close to zero you consider "practically zero", but two common choices are

- 5%, which takes almost exactly 3 time constants, and

- 1%, which takes approximately 5 times constants.

Last edited:
Ahh 5 time constants that rings a bell. thanks uart

## 1. How do I calculate the time for discharging a capacitor?

To calculate the time for discharging a capacitor, you will need to know the capacitance of the capacitor (in Farads) and the resistance of the circuit (in Ohms). The formula for calculating time is T = RC, where T is time (in seconds), R is resistance (in Ohms), and C is capacitance (in Farads).

## 2. What is the purpose of calculating the time for discharging a capacitor?

Calculating the time for discharging a capacitor is important in understanding the behavior of electrical circuits. It helps determine how long it will take for a capacitor to lose its stored energy, which is crucial in designing and troubleshooting electronic circuits.

## 3. Can I use the same formula for both charging and discharging a capacitor?

No, the formula for calculating the time for discharging a capacitor (T = RC) is different from the formula for charging a capacitor (T = 5RC). This is because the process of charging and discharging a capacitor is not symmetrical, and the resistance in the circuit may affect the charging and discharging time differently.

## 4. Is the time for discharging a capacitor affected by the voltage of the power source?

Yes, the time for discharging a capacitor is affected by the voltage of the power source. The higher the voltage, the faster the capacitor will discharge. This is because a higher voltage provides more energy for the electrons to flow through the circuit, resulting in a shorter discharging time.

## 5. How accurate is the calculated time for discharging a capacitor?

The calculated time for discharging a capacitor is an approximation and may not be 100% accurate. This is because it assumes ideal conditions, such as no resistance in the circuit and constant voltage. In real-life circuits, there will always be some resistance and fluctuations in voltage, which may affect the discharging time. However, the calculated time is still a useful tool for understanding and predicting the behavior of capacitors in circuits.

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