Capacitor RC Value - Charging/Discharging Explained

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Discussion Overview

The discussion centers on the charging and discharging behavior of capacitors in an RC circuit, specifically whether a capacitor fully charges or discharges within a time frame of 5RC, as described by the relevant formulas. The conversation includes both theoretical and practical aspects of capacitor behavior in response to a DC power source.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Ramone questions if a capacitor charges and discharges according to the calculated RC time constant and whether it fully charges/discharges at 5RC.
  • Corneo asserts that after 5RC, the voltage across the capacitor will be very close to its final value.
  • Another participant clarifies that while the voltage will be close to the final value after 5RC, it does not fully reach it, noting specific voltage percentages at each RC interval during discharge.
  • This participant emphasizes that the decay continues indefinitely, with the voltage being below 1% of its starting point after 5RC.
  • A graphic representation of the charge/discharge curve is shared to illustrate the concept further.

Areas of Agreement / Disagreement

There is no consensus on whether the capacitor fully charges or discharges at 5RC, as some participants argue it is very close but not complete, while others imply it reaches a practical limit.

Contextual Notes

The discussion includes assumptions about ideal conditions for charging and discharging, and the implications of asymptotic behavior of voltage in relation to time constants are noted but not resolved.

ramonegumpert
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Dear Experts,

I charged a capacitor that is in series with a resistor using a DC power source.
In practice, does a capacitor charge/discharge as per the calculated RC based on formula?
For example, does the capacitor really fully charge / discharge at 5RC?

Sincerely
Ramone
 
Last edited:
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Yes and Yes. If you wait 5RC, the voltage across the capacitor will be very close to its final value.
 
The really strict answer is no, although as Corneo said, the value will be very close after 5RC. This applies to charge and discharge equally, but for the moment, let's think about discharging.

When a capacitor is discharging into a resistor, the voltage will decay as follows:

After 1RC the voltage will be 36.79% of the original value.
After 2RC the voltage will be 13.53% of the original value.
After 3RC the voltage will be 4.98% of the original value.
After 4RC the voltage will be 1.83% of the original value.
After 5RC the voltage will be 0.67% of the original value.
After 6RC the voltage will be 0.25% of the original value.

This really goes on forever, but note that by 5RC the voltage is below 1% of its starting point.
Similarly on charging, 5RC takes you to within less than 1% of the final (or more correctly asymptotic) value.
 
To add to Adjusters explanation, here's a graphic look at the charge/discharge curve.
capchg3.gif

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html"
 

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