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Capacitor Question

  • Thread starter jumbogala
  • Start date
1. 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?


2. Homework Equations
Not sure - maybe q = qf (1-e-t/RC)

3. 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

Homework Helper
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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*Qo

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 VR + VC then ...

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

Homework Helper
3,079
4
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

Homework Helper
3,079
4
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.
 
Oh okay, that makes sense.

Thank you!
 

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