Capacitors

    Cards (21)

    • What is a capacitor?

      A component used to store electrical charge
    • How does a capacitor work?

      There are two conductive metal plates connected to a voltage supply with a dielectric between them. Charge builds up on the two plates creating a potential difference between them.
    • What is the equation for Capacitance, C

      C = Q/V
    • What is the unit of Capacitance?

      Farad (F)
    • What is the equation for energy in a capacitor?

      E = 1/2 QV
    • What are the alternate equations for energy in a capacitor?

      E = 1/2 C V^2 and E = Q^2 / 2C
    • How is total Capacitance in series calculated?

      1/Ct = 1/C1 + 1/C2 ....
    • How is total Capacitance in parallel calculated?

      Ct = C1 + C2 ....
    • How does current change when a capacitor is charging?

      The current decreases exponentially to zero
    • How does voltage change when a capacitor is charging?

      The voltage increases to a maximum
    • How does current change when a capacitor discharges?

      The current decreases exponentially to zero
    • How does potential difference change when a capacitor discharges?

      The potential difference decreases to zero by exponential decay
    • What is a capacitor used for?

      Charge is stored creating a build-up of electrical potential energy which is used for a backup release of energy if the power fails.
    • What is the time constant, τ ?

      The time constant τ is the time taken for the current, charge stored, or p.d. to fall to 1/e (about 37%) of its initial value.
    • What is the equation for the time constant?

      τ = RC

      Time constant = Resistance x Capacitance.
    • What is the general equation for capacitors discharging?

      x = x₀(1 - e^(-t/CR))
    • Proof that total capacitance in parallel is the sum of capacitance of individual capacitors
      - Total charge stored, Q is equal to the sum of individual charges (Qt = Q1 +Q2 + Q3).
      - P.d. across each capacitor is the same as they are in parallel V1 = V2 = V3
      - C = Q/V -> Q = CV therefore:
      VCt = VC1 + VC2 + VC3....
      V cancels out leaving Ct = C1 + C2 + C3...
    • Proof of the result for total capacitance in series
      - Kirchhoff's second law:
      Vt = V1 + V2 + V3
      - charge stored by each capacitor is the same
      Q = Q1 = Q2
      - C = Q/V -> V = Q/C
      - Q/Ct = Q/C1 + Q/C2 ....
      Q cancels leaving 1/Ct = 1/C1 + 1/C2 ....
    • How is energy stored in a capacitor?

      - Work must be done to push electrons onto the negative plate
      - Work must also be done to pull electrons from the positive plate
      - This work is stored as energy in the capacitor
    • Plotting a graph of V against Q, what is the area under the graph?
      Electrical potential energy as area = 1/2 QV = E
    • What are the main uses of capacitors?

      - capacitors can be used to smooth output voltage when arranged in a certain way
      - capacitors are used in mobile phone screens to detect touch
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