Charge after three time constants?

In summary, "Charge after three time constants" refers to the maximum charge that can be stored on a capacitor after it has been charging for three times its time constant. This is calculated using the equation Q = Qmax(1-e^(-3)), where Qmax is the maximum charge the capacitor can hold. This information is important for designing and analyzing electronic circuits involving capacitors, and after three time constants, the capacitor will reach 95% of its maximum charge. This charge can be altered by changing the values of resistance, capacitance, or initial voltage on the capacitor.
  • #1
Keeeen
24
0

Homework Statement


A 10V supple is connected to a 2.2μF capacitor in series with a 10kΩ resistor. To what value will it have charged after three time constants?


Homework Equations


I know that T=RC but I have no idea beyond this point


The Attempt at a Solution


T=RC
T=2.2μF*10kΩ
T=22

the rest is unknown to me, if someone could explain it to me that would be awesome.
 
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  • #2
Either find the expression for a charging capacitor or derive it yourself. It's a simple linear, first-order, constant-coefficient differential equation. (Sum currents to zero at the capacitor-resistor junction.)
 

1. What is "charge after three time constants"?

"Charge after three time constants" refers to the amount of charge that has built up on a capacitor after it has been charging for three times its time constant. This is typically represented by the equation Q = Qmax(1-e^(-3)), where Qmax is the maximum charge the capacitor can hold.

2. How do you calculate the charge after three time constants?

The charge after three time constants can be calculated using the equation Q = Qmax(1-e^(-3)). This equation takes into account the maximum charge the capacitor can hold (Qmax) and the time constant (RC). The time constant is calculated by multiplying the resistance (R) and capacitance (C) of the circuit.

3. Why is "charge after three time constants" important?

"Charge after three time constants" is important because it represents the maximum charge that can be stored on a capacitor. This information is useful for designing and analyzing electronic circuits that involve capacitors, such as filters, oscillators, and power supplies.

4. What happens to the charge after three time constants?

After three time constants, the charge on the capacitor will reach 95% of its maximum value. This means that the capacitor has reached its steady state and will no longer continue to charge. The remaining 5% of charge will continue to build up very slowly over time, but can be considered negligible for practical purposes.

5. Can "charge after three time constants" be altered?

Yes, the charge after three time constants can be altered by changing the values of resistance or capacitance in the circuit. A larger resistance or capacitance will result in a longer time constant, and therefore a different charge after three time constants. Additionally, the initial voltage on the capacitor can also affect the charge after three time constants.

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