Charge after three time constants?

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SUMMARY

The discussion centers on the charging behavior of a 2.2μF capacitor connected to a 10kΩ resistor with a 10V supply. The time constant (T) is calculated as T = RC, resulting in T = 22 milliseconds. After three time constants, the voltage across the capacitor can be determined using the formula V(t) = V0(1 - e^(-t/T)), leading to a charge of approximately 9.5V after 66 milliseconds. This analysis utilizes fundamental principles of first-order linear differential equations.

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  • Understanding of RC circuits
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  • Basic knowledge of exponential functions
  • Ability to solve first-order differential equations
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Keeeen
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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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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.)
 

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