# RC Circuits charging/discharging

1. Nov 6, 2013

### CollegeStudent

1. The problem statement, all variables and given/known data

Plot I_r vs. time and Q_c vs. time starting from when the switch is moved from its lower position to its upper position. Label both axes with numbers and units. Show three time constants. Assume that the capacitor is initially uncharged. After the circuit reaches its final state the switch is moved to its lower position. Plot both I_r and Q_c vs. time starting from when the switch is first closed to it lower position. Again show numbers, units, etc. How long will it take for the capacitor to be 50% discharged? 90%?

2. Relevant equations

Charging circuit .... q = Q_f - Q_f * e^-t/RC
Discharging Circuit q = Q_o * e^-t/RC

3. The attempt at a solution

I'm assuming that where the switches are drawn to be the "Lower position" so this is the moment right after the switch is flipped.

Since the question states the capacitor initially is uncharged, For all 4 circuits the graph of I_r and Q_c vs time would look like

I_r - starts at the max value and exponentially decays
Q_c - starts at 0 and exponentially grows

Right? Because the capacitor has to charge before this whole process gets to its "final state" and begins to discharge...or am I off here?

2. Nov 6, 2013

### rude man

You've described the charging cycle but not the discharging cycle.

What are the actual numbers for I_r max and Q_c max?

3. Nov 6, 2013

### Staff: Mentor

Circuit 4 has two switches, is it to be included in this question? If so, how to interpret the instructions?

In circuits 1 and 2 I can see how the capacitors can be initially uncharged if the switch has been in the lower position for some time before being moved to the upper position. In circuit 3, however, the lower position would close the switch and charge the capacitor. So the assumption of an uncharged capacitor for the switch in the lower position appears to be incorrect. Is the problem statement exactly as it was given to you?