The Physics
Hypertextbook
Opus in profectus

Capacitors in Circuits

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Problems

practice

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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