Time constant and capacitors

In summary, the rate at which a capacitor charges and discharges is determined by resistance and capacitance in a circuit. The time constant, equal to RC, is the time it takes for the charge on a discharging capacitor to decrease to 37% of the initial charge (Qo). This is also equivalent to the time it takes for the charge on a charging capacitor to increase by 63% of Qo. This relationship is derived from solving the differential equation for an RC circuit, which results in exponential expressions for charge, current, and voltage. The constant 'e-1' in this solution is where the 63% value comes from. In summary, the time constant is the time it takes for the charge to reach
  • #1
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So the rate at which a capacitor charges and discharges is dependent on resistance in a circuit and the magnitude of capacitance of the capacitor? So the time constant is equal to RC. So using this equation where Q=Qoe-t/RC ,time constant is the time taken (when the capacitor is discharging) for charge on a capacitor (Q) to decrease to 37% of Qo ( i.e. charge on the capacitor when it is is fully charged). But I've been reading around and what I don't get is how the time constant is also equal to the time taken for the charge (Q) on a charging capacitor to increase by 63% of Qo . If this makes any sense, would be good if someone could maybe explain it mathematically as well i.e. how 'e' is involved?
 
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  • #2
Hannah7h said:
i.e. how 'e' is involved?
Have you studied calculus?
 
  • #3
cnh1995 said:
Have you studied calculus?

Um haven't studied it in much detail, but I could give it a go
 
  • #4
Hannah7h said:
Um haven't studied it in much detail, but I could give it a go
Well, KVL equation for an RC circuit is a differential equation. Solving that differential equation, you get exponential expressions for charge, current and voltage.
 
  • #5
cnh1995 said:
Well, KVL equation for an RC circuit is a differential equation. Solving that differential equation, you get exponential expressions for charge, current and voltage.

Ok so... how does this relate to the 63% of Qo?
 
  • #6
Hannah7h said:
time constant is the time taken (when the capacitor is discharging) for charge on a capacitor (Q) to decrease to 37% of Qo
Or in other words, time taken to lose 63% of Q0.
Hannah7h said:
on a charging capacitor to increase by 63% of Qo
You can see that the time taken to gain a charge of 0.63Qo (while charging) is equal to the time taken to lose the same charge of 0.63Q0(while discharging). It's obvious, isn't it?
 
  • #7
Hannah7h said:
Ok so... how does this relate to the 63% of Qo?
If you are asking where 63% comes from, it comes from the constant 'e-1' in the solution to the differential equation of the RC circuit.
 
  • #8
the time constant is the time taken to get to within 37% of the final value.
In decay the final value is 0%!
In growth the final value is 100%
 
  • #9
cnh1995 said:
If you are asking where 63% comes from, it comes from the constant 'e-1' in the solution to the differential equation of the RC circuit.

Ok that was pretty obvious now I look at it, thank you for explaining it otherwise I probably wouldn't have got there lol
 
  • #10
lychette said:
the time constant is the time taken to get to within 37% of the final value.
In decay the final value is 0%!
In growth the final value is 100%

Yep this makes sense, thanks!
 

1. What is a time constant?

A time constant is a measure of how quickly a capacitor charges or discharges. It is equal to the product of the capacitance and the resistance in an electrical circuit.

2. How is the time constant calculated?

The time constant (τ) is calculated by dividing the capacitance (C) by the resistance (R), or τ = C/R. It is measured in seconds.

3. What is the relationship between time constant and charging/discharging of a capacitor?

The time constant determines the rate at which a capacitor charges or discharges. A larger time constant means a slower charging or discharging process, while a smaller time constant results in a faster process.

4. How does the time constant affect the behavior of a capacitor in a circuit?

The time constant affects the behavior of a capacitor by determining the amount of time it takes for the capacitor to reach a certain level of charge or discharge. It also determines the shape of the charging/discharging curve, with a larger time constant resulting in a more gradual curve and a smaller time constant resulting in a steeper curve.

5. How can the time constant be used in circuit analysis?

The time constant can be used in circuit analysis to predict the behavior of a capacitor in a circuit over time. It can also be used to calculate the voltage or current at different points in the charging/discharging process.

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