Capacitor circuit time constant problem

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SUMMARY

The discussion centers on calculating the time it takes for a capacitor to charge to one quarter of its initial value using the time constant formula (τ = RC). The correct approach involves using the equation Qf = 0.25 * Vinitial * C, leading to the conclusion that the time required is t = ln(4) * (-RC), which equals approximately 1.39 seconds. A participant initially miscalculated by using Vf instead of Vinitial, highlighting the importance of accurate variable representation in capacitor discharge equations.

PREREQUISITES
  • Understanding of capacitor charging and discharging principles
  • Familiarity with the time constant formula (τ = RC)
  • Knowledge of natural logarithms and their application in exponential decay
  • Basic circuit analysis skills
NEXT STEPS
  • Review the derivation of the capacitor discharge equation Vc = Vo * e^(-t/RC)
  • Learn about the significance of initial voltage (Vinitial) in capacitor calculations
  • Explore practical applications of time constants in RC circuits
  • Study the behavior of capacitors in different circuit configurations
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Students studying electrical engineering, educators teaching circuit theory, and anyone looking to deepen their understanding of capacitor behavior in electronic circuits.

helppls

Homework Statement


How long does it take in time constants ( = RC) for the charge on the capacitor in the circuit
shown below to reach one quarter its initial value?

Homework Equations


C=Q/V
time constant=RC
Vc = Vo * (e)^(-t/RC)

The Attempt at a Solution


From C=Q/V
I get
Q=VC
so for the final charge, Qf, to be 1/4 of it's value
Qf= 0.25 * Vf * C
rearrange to get
Vf = 4 * Qf / C
then I assume I can ignore Qf and C and plug in 4 to the discharging equation:

4= 1 * e^(-t/RC)
then take the natural log of both sides

ln(4) = -t/RC
t= ln(4) * (-RC) = 1.39s
the problem: my friend got a different answer: ln(1/4)s , which makes sense because it yields -1.39s (and is then multiplied by -1) , so I am wondering if I did something incorrectly?

I also am not sure if either of us did it correctly because it is asking for the answer in time constants? That being said it should happen between 1 and 2 time constants because at 1 it would be at 36%, and 2 it would be at 13%.

thanks in advance for your help.
 

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helppls said:
t= ln(4) * (-RC) = 1.39s
That is incorrect. Your friend got it right.
helppls said:
Qf= 0.25 * Vf * C
No. It should be
Qf= 0.25*Vinitial*C.
 
ahhhh, thank you!
 

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