Capacitance of circuit & RC time constant

In summary, to determine the equivalent capacitance of the circuit, you need to find q0 and q through the equation q=CV. TheAttempt at a Solution determined that the equivalent capacitance is 20*10^-6 Farads.
  • #1
dewdrop714
17
0
1. The problem statement

http://s685.photobucket.com/albums/vv212/dewdr0p714/?action=view&current=5circuittakehometest1.jpg

1) Determine the equivalent capacitance of the circuit

2) How many RC time constants are needed for the charge on the capacitors to reach 75% of their final charge?



2. Homework Equations

q= q0 (1 - e^-t/RC)
q=CV


3. The Attempt at a Solution

I tried to find the equivalent capacitance...this was my method but I am not sure if it is correct.

Equiv Capac = (15*10^-6)(10*10^-6) + (10*10^-6)(10*10^-6) + (15*10^-6)(10*10^-6) / (10*10^-6) + (10*10^-6)

Equiv Capac = 20*10^-6 Farads

For the RC time constants question, I think I need the capacitance to be able to solve it and with the capacitance that I got, I could find q thru the equation q=CV...after that I am unsure about how to proceed with question #2. Does the q get inputted for q or q0?
 
Last edited:
Physics news on Phys.org
  • #2
Sorry to keep you waiting, but no one can see your picture until a member of the staff authorizes it. If you are in a hurry, you could describe the circuit, or post your picture to a service such as photobucket.com and then give us a link to it.
 
  • #3
Oh thanks i didn't know that. I posted it on photobucket and here's the link:

http://s685.photobucket.com/albums/vv212/dewdr0p714/?action=view&current=5circuittakehometest1.jpg
 
  • #4
I got the same answer for the total capacitance.
For the 2nd part, Q=CV says 75% charge is 75% Voltage, so don't you just have to look at the factor (1 - e^-t/RC) ?
You could try t = RC, 2RC, 3RC, etc until you the factor is .75 or more.
Better, of course to make the factor equal to .75 and solve for t. Logs?
 
  • #5
Hmm I don't quite understand what you mean. I get the part about q being proportional to v so .75q~.75v. But being that the equation is q=q0(1-e^-t/RC), what would q0 be? And the whole RC time constant thing confuses me completely...like how can t=RC?
 
  • #6
Okay, you'd rather work with q= q0 (1 - e^-t/RC).
If you put in t = 0, you get q = 0.
put in t = RC and you get q = .63 q0, so 63% charged.
At t = 2RC, you get q = .86 q0, so 86% charged.

Set q = .75q0 to get .75 = (1 - e^-t/RC)
Solve that for t to get somewhere between 1RC and 2RC where it is 75% charged.
 
  • #7
thank you for your help i figured it out! =]
 

Related to Capacitance of circuit & RC time constant

What is capacitance and how does it affect a circuit?

Capacitance is the ability of a capacitor to store electrical energy in an electric field. It is measured in Farads (F) and determines how much charge can be stored on the capacitor for a given voltage. In a circuit, capacitance can affect the flow of current and the amount of charge that can be stored in the circuit.

What is the formula for calculating capacitance?

The formula for capacitance is C=Q/V, where C is capacitance in Farads, Q is the charge stored on the capacitor in Coulombs, and V is the voltage across the capacitor in Volts.

What is the RC time constant and how is it calculated?

The RC time constant is a measure of how quickly a capacitor charges or discharges in a circuit. It is calculated by multiplying the resistance (R) in Ohms by the capacitance (C) in Farads, giving a time constant in seconds (RC = R * C).

How does the RC time constant affect the behavior of a circuit?

The RC time constant determines the rate at which a capacitor charges and discharges in a circuit. A smaller time constant means the capacitor will charge or discharge more quickly, while a larger time constant means it will take longer. This can affect the time it takes for a circuit to reach a steady state or the speed at which a signal can be transmitted through the circuit.

What factors can affect capacitance and the RC time constant in a circuit?

Capacitance can be affected by the physical properties of the capacitor, such as the size and material of the plates, as well as the distance between them. The RC time constant can be affected by the resistance and capacitance values in the circuit, as well as external factors such as temperature and humidity. Any changes in these factors can alter the behavior of the circuit and affect the overall capacitance and time constant.

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
399
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
859
  • Introductory Physics Homework Help
Replies
4
Views
978
  • Introductory Physics Homework Help
Replies
2
Views
1K
Replies
19
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
Back
Top