Capacitors in Circuits

Problems

practice

1. Write something.
2. Write something.
3. Write something.
4. Write something completely different.

numerical

1. A 12 V battery is connected to two resistors and two capacitors as shown in the diagram on the right. The resistors and the capacitors were chosen so that points A and B are at the same potential. Determine…
   1. the potential drop across the 1 Ω resistor
   2. the potential drop across the 3 Ω resistor
   3. the current through the 1 Ω resistor
   4. the current through the 3 Ω resistor
   5. the potential drop across the 1 μF capacitor
   6. the potential drop across the unknown capacitor
   7. the charge stored in the 1 μF capacitor
   8. the charge stored in the unknown capacitor
   9. the capacitance of the unknown capacitor
2. The circuit below is made of three 2 Ω resistors, three 2 µF capacitors, and a 12 V battery. There is a rotating switch at the top and bottom of the circuit made out of wire in the shape of a "T". Initially, all capacitors are uncharged and both switches are midway between two positions.

   

   	currents through…			charges on…
   	R1	R2	R3	C1	C2	C3
   initial conditions	0 A	0 A	0 A	0 µC	0 µC	0 µC

   The two switches are then simultaneously rotated into a series of three positions, one after the other, and held there for a "long time". For each position, determine the current through each resistor and the charge on each capacitor at the moment the circuit is completed and then after a "long time".

   1. First position

      

      First position

      	currents through…			charges on…
      	R1	R2	R3	C1	C2	C3
      circuit completed
      after a long time

   2. Second position

      

      Second position

      	currents through…			charges on…
      	R1	R2	R3	C1	C2	C3
      circuit completed
      after a long time

   3. Third position

      

      Third position

      	currents through…			charges on…
      	R1	R2	R3	C1	C2	C3
      circuit completed
      after a long time