Capacitor circuit time constant problem

In summary, the time it takes for the charge on the capacitor in the circuit to reach one quarter of its initial value is approximately ln(1/4)*RC seconds. It is important to note that this should happen between 1 and 2 time constants, with 1 time constant corresponding to 36% and 2 time constants corresponding to 13%.
  • #1
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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  • #2
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.
 
  • #3
ahhhh, thank you!
 

FAQ: Capacitor circuit time constant problem

What is a capacitor?

A capacitor is an electrical component that stores energy in an electrical field. It is made up of two conductive plates separated by an insulating material, known as a dielectric.

What is a capacitor circuit time constant problem?

A capacitor circuit time constant problem is a type of calculation that is used to determine the rate at which a capacitor charges or discharges in an electrical circuit. It takes into account the capacitance of the capacitor and the resistance of the circuit.

How do you calculate the time constant of a capacitor circuit?

The time constant of a capacitor circuit is calculated by multiplying the capacitance (in farads) by the resistance (in ohms). The resulting value is measured in seconds and represents the time it takes for the capacitor to charge or discharge by 63.2% of its maximum value.

Why is the time constant important in capacitor circuits?

The time constant is important because it determines the speed at which a capacitor charges or discharges. It is also used in the design and analysis of circuits to determine the behavior of the capacitor and the circuit as a whole.

What are some practical applications of capacitor circuit time constant problems?

Capacitor circuit time constant problems are used in a variety of practical applications such as in electronic devices, power supplies, and audio equipment. They are also used in timing circuits, filters, and other electronic circuits to control the rate of charging and discharging of capacitors.

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