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Series grouping

  • Charge on each capacitor remains same and equals to the main charge supplied by the battery but potential difference distributes, i.e., V = V1 + V2 + V3
  • Equivalent capacitance, 63801.png
    or 63807.png
  • In series combination, potential difference and energy distributes in the reverse ratio of capacitance, i.e.,
  • If two capacitors having capacitances C1 and C2 are connected in series then
  • If n identical capacitors each having capacitances C are connected in series with supply voltage V then, equivalent capacitance Ceq = C/n and potential difference across each capacitor, V ’ = V/n.
  • If n identical plates are arranged as shown in Fig. 11, they constitute (n – 1) capacitors in series. If each capacitors having capacitance ε0A/d, then,
    Fig. 11
    In this situation, except two extreme plates each plate is common to adjacent capacitors.

Parallel grouping

  • Potential difference across each capacitor remains same and equal to the applied potential difference but charge distributes, i.e., Q = Q1 + Q2 + Q3
  • Equivalent capacitance, C­eq = C1 + C2 + C3
  • In parallel combination, charge and energy are distributed in the ratio of capacitance, i.e., Q ∝ C and U C
  • If two capacitors having capacitance C1 and C2 respectively are connected in parallel then Ceq = C1 + C2
    63863.png and 63877.png
  • If n identical capacitors are connected in parallel, then equivalent capacitance, Ceq = nC and charge on each capacitor, Q’ = Q/n.
    If n identical plates are arranged such that the even-numbered plates are connected together and odd numbered plates are connected together, then (n – 1) capacitors will be formed and they will be in parallel grouping (Fig. 12).
    Fig. 12
    Equivalent capacitance, C’ = (n – 1) C
    where C = capacitance of a capacitor = ε0A/d.
Some Important Points
  • It is a very common misconception that a capacitor stores charge but actually a capacitor stores electric energy in the electrostatic field between the plates.
  • Two plates of unequal area can also form a capacitor because effective overlapping area is considered.
    Fig. 13
  • If two plates are placed side by side, then three capacitors are formed. One between distant Earthed bodies and the first face of the first plate, the second between the two plates and the third between the second face of the second plate and distant Earthed objects. However, the capacitances of the first and third capacitors are negligibly small in comparison to that between the plates which is the main capacitance.
    Fig. 14
  • Capacitance of a parallel plate capacitor depends upon the effective overlapping area of plates (C ∝ A), separation between the plates (C ∝ 1/d) and dielectric medium filled between the plates. While it is independent of charge given, potential raised or nature of metals and thickness of plates.
  • The distance between the plates is kept small to avoid fringing or edge effect (non-uniformity of the field) at the boundaries of the plates.
    Fig. 15

When dielectric is partially filled between the plates

If a dielectric slab(s) is/are inserted between the plates, then
Case I Capacitance of the capacitor
Fig. 16
Case II Capacitance of the capacitor
Fig. 17
Case III Capacitance of the capacitor
Fig. 18

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