Calculating Potential Difference on A Capacitor, RC Circuits

[cwatki14]

The circuit of Figure P.72 has been turned on for a long time, so that you can ignore the transient behavior of the capacitor. Voltage of Battery V = 31 V

(e) What is the potential difference across the capacitor C (C = 9 µF)?

I thought about using Kirchoff Voltage Law, but I also though that when a capacitor is fully charged the potential difference should be equal to that on the battery, but the computer said that was wrong. It also is not zero. Any ideas?

 

[Delphi51]

Initially the uncharged capacitor will have very voltage, so a lot of current will flow that way. But as it becomes charged its voltage rises until no current at all flows into it. The resistance of that part of the circuit is effectively infinite, so you just ignore it. The circuit you have left is the battery driving current into the 2 and 3 ohm resistors in series. Calculate that current and the voltage across the 3 ohm resistor. Since there is no current through the 1 ohm resistor, it will have no voltage drop V=IR across it and so you know the voltage on the capacitor.

 

[tomcue]

The potential difference across a capacitor in a circuit can be calculated using the formula V = Q/C, where V is the potential difference, Q is the charge on the capacitor, and C is the capacitance. In this case, the capacitor has a capacitance of 9 µF and the battery has a voltage of 31 V.

Since the circuit has been turned on for a long time, the capacitor is fully charged and the charge on it is equal to the charge on the battery. Therefore, we can calculate the charge on the capacitor using the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage.

Plugging in the values, we get Q = (9 µF)(31 V) = 279 µC.

Now, we can use this value to calculate the potential difference across the capacitor using V = Q/C.

V = (279 µC)/(9 µF) = 31 V

As you can see, the potential difference across the capacitor is indeed equal to the voltage of the battery. It is not zero because even though the capacitor is fully charged, it still has a potential difference across its plates.

In summary, to calculate the potential difference across a capacitor in a circuit, you can use the formula V = Q/C, where Q is the charge on the capacitor and C is the capacitance. In this case, the potential difference across the capacitor is equal to the voltage of the battery.