Capacitor Question: Voltage & Limiting Voltage

[jumbogala]

Homework Statement

A circuit is connected to charge a capacitor. The switch in the circuit is initially open, then closed at t = 0.

As t --> infinity, what is the voltage across the capacitor?

When does it reach 60 % of this limiting voltage?

Homework Equations

Not sure - maybe q = q_f (1-e^-t/RC)

The Attempt at a Solution

I think as t --> infinity, the voltage across the capacitor will be equal to the emf of the battery.

But I don't know what limiting voltage is, or how you find it. The only equation I could find involving time is the one above, but I'm not sure if or how that applies to this question.

 

[LowlyPion]

I think as t --> infinity, the voltage across the capacitor will be equal to the emf of the battery.

Correct. When t ⇒ ∞ you have 1 - 1/e^∞ = 1 - 0 = 1*Q_o

When the charge on the capacitor approaches fully charged there's no charge flowing right? (dQ/dt ⇒ 0)

So what does that mean for the voltage drop across the resistor R of the RC? Since V of the emf is V_R + V_C then ...

As to the time that needs to be used to determine the 60% level. (The "When" part of the second question.)

 

[jumbogala]

So there's no charge flowing because dQ isn't changing (it can't get any bigger than Qo), is that correct?

If there's no current flowing, then voltage is zero too because V = IR?

I'm confused about the statement Vr + Vc =/

 

[jumbogala]

I think I might just have figured it out. If I use the formula

Q = CV, where Q is the charge on the capacitor, C is capacitance and V is voltage.

60 % of the voltage occurs when there is 60 % of the Qo, since C is a constant for any capacitor.

Then I would use the formula 0.60q = q(1-e-t/RC) and solve for t.

Hm... except I just realized I don't know the values of R or C.

 

[LowlyPion]

So there's no charge flowing because dQ isn't changing (it can't get any bigger than Qo), is that correct?

If there's no current flowing, then voltage is zero too because V = IR?

I'm confused about the statement Vr + Vc =/

The voltage across your emf is the sum of the voltages across the R and the C. They are in series right? So that makes a Voltage loop that must be satisfied. If the Voltage of the R ⇒ 0 then that means that the Voltage of the Capacitor must be the emf Voltage.

 

[LowlyPion]

I think I might just have figured it out. If I use the formula

Q = CV, where Q is the charge on the capacitor, C is capacitance and V is voltage.

60 % of the voltage occurs when there is 60 % of the Qo, since C is a constant for any capacitor.

Then I would use the formula 0.60q = q(1-e-t/RC) and solve for t.

Hm... except I just realized I don't know the values of R or C.

Yes that's correct.

You can give your answer in terms of RC. At what value of RC does the equation yield 60% voltage is what they are asking.

 

[jumbogala]

Oh okay, that makes sense.

Thank you!