Potential difference across a capacitor

[issacnewton]

Hi

I have a question about part a). Using Kirchoff's rules, I got the expression for the charge
on the capacitor during the charging phase.

$$q\, = \, 6C \left [ 1- exp ( - \frac{5t}{12C})\right ]$$

and as t goes to infinity, we see that

$$q = 6C$$

so the potential difference across the capacitor would be 6 V . But then left plate of the capacitor is at same potential as the positive terminal of the battery , since there is no potential difference across any resistor (as there is no current) and the right plate would be
at the same potential as the negative terminal of the battery. So potential difference across
the capacitor should turn out to be 10 V. But I checked my answer and the potential difference is 6 V. So what's happening here ?

thanks

 

[SammyS]

When the capacitor is fully charged, no current flows through it. However, current continues to flow through all the resistors, as long as the battery is connected.

1 Amp flows through the 8Ω and 2Ω resistors. 2 Amps flow through the 1Ω and 4Ω resistors. From these values you check that indeed, the capacitor has 6 V across it.

 

[issacnewton]

Thanks Sammy,

that makes solving the part a) even simpler. I didn't think of it before