Bench notes / Timing

RC Discharging Voltage: the method, worked through

An initially charged capacitor loses voltage exponentially through an ideal resistance.

Initial voltage compared with the result of RC Discharging Voltage; the example conditions stay fixed
Figure 1. Calculated scenarios for rc discharging voltage. The highlighted point uses the example input. Lines connect sampled points and do not imply valid fractional counts.

Start with the relationship

The question this tool answers is specific: given initial voltage, resistance, capacitance, time, what value follows from the stated model? The result is expressed in V. The calculation below makes that relationship visible, so the answer can be checked independently instead of accepted as an unexplained number.

initial × exp(−time / RC)

Check the component connections and unit prefixes before copying a result into a circuit notebook. These tools describe ideal, introductory circuits. They do not replace datasheets, thermal checks, isolation requirements or qualified design work, and they are not intended for mains installation decisions.

A worked example

Use the following values as a reproducible starting point. They are illustrative inputs, not measurements of your situation or a recommendation for a particular project. The calculator opens with the same values, making it possible to compare a manual calculation with the on-screen answer.

InputExample valueUnit
Initial voltage5V
Resistance10kΩ
Capacitance100µF
Time1s

Substitute these quantities into the displayed relationship: initial voltage = 5 V; resistance = 10 kΩ; capacitance = 100 µF; time = 1 s. Carry out the operations before rounding the final value. This gives 1.839397 V. The number is a result for this particular set of inputs; changing the measurement basis or the conditions can change its practical meaning.

What changes when an input changes?

In the illustrated range, changing initial voltage from 3 to 7 V moves the result from 1.103638 to 2.575156 V. The output increases between those endpoints. The table gives intermediate samples so you can see whether the response is smooth, stepped or nonmonotonic; the endpoints alone do not establish that behaviour.

Every other input keeps the value shown in the example table. This controlled comparison isolates one relationship at a time. For a real decision, try a lower, central and higher plausible input instead of treating an uncertain measurement as perfectly exact.

Initial voltage (V)Result (V)
31.103638
41.471518
51.839397
62.207277
72.575156

The assumption that matters

Leakage, measurement equipment and extra circuit branches can alter the discharge time.

A valid numerical result only means the entered values can be evaluated by this formula. It does not confirm that the formula describes every feature of the real situation. Read the unit labels, check the measurement method and keep the specific limitation above with the result when sharing it.

Use the result in your own work

Open the calculator, replace the example values and select Calculate. The result is evaluated on your device. Reset example restores this article's scenario, while Copy result keeps the quantity and unit together. If an input is outside the model's allowed range, correct it before interpreting the output.

Keep more digits during a chain of calculations than you show in a finished note. Displayed values are rounded for readability; extra decimals do not make a rough measurement more accurate. When your decision depends on a tight tolerance, compare the original measurements and assumptions before relying on the last displayed digit.

Open RC Discharging Voltage

Further reading & method notes

OpenStax — mathematics and physics learning resources provides background for this subject. This article's numerical examples and chart were calculated from the formula shown above. See the editorial policy for how this collection presents assumptions and corrections.

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