Charging/discharging capacitor circuit

[Juan Pablo]

Homework Statement

The circuit http://imgur.com/WSd2L. I'm asked to find the current and voltage on the capacitor using diff. eqns. It says that I can assume that the capacitor doesn't have charge at the beginning for the charging circuit and the capacitor in the only source of voltage for the discharge circuit.

The Attempt at a Solution

$$V - R \frac{dQ}{dt} = 0$$

For the charge circuit and

$$R\frac{dQ}{dt} + \frac{Q}{C} = 0$$

for the discharge circuit.

I'm not sure If I did this correctly. To get the current I plan to differentiate the charge function I get. For the Voltage maybe Ohm's law? Sorry if this is completely wrong BTW.


Thanks in advance!

 

[anathema]

Thank you for your post. It seems like you have the right idea for solving this problem. To find the current, you can differentiate the charge function as you mentioned. To find the voltage, you can indeed use Ohm's law, as the resistor and capacitor are in series. However, keep in mind that for the discharge circuit, the capacitor is the only source of voltage, so the voltage across the resistor will be 0.

Also, make sure to keep track of the initial conditions for each circuit. For the charge circuit, the initial charge on the capacitor is 0, so Q(0) = 0. For the discharge circuit, the initial voltage on the capacitor is V, so Q(0) = CV. This will help you solve the differential equations correctly.

I hope this helps. Good luck with your work!