RC Circuits, time to charge a capacitor

[iiiiaann]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

I really don't even know where to start with this one

 

[SammyS]

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 ?

 

[iiiiaann]

the charge on the capacitor would be

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

if the potential difference were E

 

[SammyS]

... At what time is the electric potential across the capacitor equal to that across the resistor? ...

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

 

[iiiiaann]

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

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

 

[SammyS]

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

Yes, according to Kirchhoff.

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

 

[iiiiaann]

Would it just be 1/2 E?

 

[iiiiaann]

where do i go from here?

 

[SammyS]

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

 

[iiiiaann]

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

 

[SammyS]

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

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

 

[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

 

[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?

 

[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