# RC Circuits, time to charge a capacitor

1. Oct 17, 2011

### iiiiaann

1. The problem statement, all variables and given/known data
Switch S in the figure below is closed at time t = 0, to begin charging an initially uncharged capacitor of capacitance C = 13.0 µF through a resistor of resistance R = 24.0 . At what time is the electric potential across the capacitor equal to that across the resistor?

2. Relevant equations

i = dq/dt
q = CE(1-e^-t/RC)

3. The attempt at a solution

2. Oct 17, 2011

### SammyS

Staff Emeritus
I assume that E is the EMF of the battery.

Is q the charge on the capacitor at time, t ?

How much charge would be on this capacitor of the potential difference across it was E ?

3. Oct 17, 2011

### iiiiaann

the charge on the capacitor would be

Q = CV = (13e-6)(E)

if the potential difference were E

4. Oct 17, 2011

### SammyS

Staff Emeritus
At the above time, how do these two potentials compare with E , the electric potential provided by the battery?

5. Oct 17, 2011

### iiiiaann

I'm not sure i follow what you are saying? Would the combination of the 2 be equal to E?

6. Oct 17, 2011

### SammyS

Staff Emeritus
Yes, according to Kirchhoff.

Since the two are equal, what is the electric potential across the capacitor ?

7. Oct 17, 2011

### iiiiaann

Would it just be 1/2 E?

Last edited: Oct 17, 2011
8. Oct 17, 2011

### iiiiaann

where do i go from here?

9. Oct 17, 2011

### SammyS

Staff Emeritus
If the electric potential on the capacitor is E/2, then how much charge is on the capacitor?

10. Oct 17, 2011

### iiiiaann

the charge is Q = CV which would be 13uF * E / 2

11. Oct 17, 2011

### SammyS

Staff Emeritus
So, solve this equation for t when q = C(E/2)

q = CE(1-e^-t/RC)

12. Oct 17, 2011

### iiiiaann

C(E/2) = CE(1-e^-t/RC)
1/2 = 1 - e^-t/RC
e^-t/RC = 1/2
-t/RC = ln(1/2)
-t = ln(1/2) * RC
t = -1 * ln(1/2) * RC

t = -1 * -.6931 * 24 * 13e-6 = 0.000216 s = 0.216 ms

Thanks again for the help, these forums (you especially) are fantastic

13. Jan 7, 2012

### Gumba

Hello, may I ask what kind of equation q = CE(1-e^-t/RC) is? Does the problem give it as the equation which determines the time to charge of the capacitor through this RC circuit? How do they get to such an equation?

14. Jan 7, 2012

### technician

If you check your capacitor equations you will find a more convenient expression for the voltage across a capacitor during charging.
V = Vmax(1 - e^-t/RC) so you can calculate the voltage across the capacitor t sec after switch on.
The charge equation is the same exponential form
Q = Qmax(1-e^-t/RC)
hope this helps