Five capacitor of capacitance C are connected (I) in series and then (II) in parallel. The ratio of equivalent capacitance in case (I) to that in case (II) is:

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  1. 1 : 5
  2. 5 : 1
  3. 1 : 25
  4. 25 : 5

Answer (Detailed Solution Below)

Option 3 : 1 : 25
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CONCEPT:

Capacitor:

  • The capacitor is a device in which electrical energy can be stored.
    • In a capacitor two conducting plates are connected parallel to each other and carrying charges of equal magnitudes and opposite sign and separated by an insulating medium.
    • The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or semi-conductor called a dielectric.​

1. Capacitors in series

  • When two or more capacitors are connected one after another such that the same charge gets generated on all of them, then it is called capacitors in series.
  • The net capacitance/equivalent capacitance (C) of capacitors in series is given by,

2. Capacitors in parallel

  • When the plates of two or more capacitors are connected at the same two points and the potential difference across them is equal, then it is called capacitors in parallel.
  • The net capacitance/equivalent capacitance (C) of capacitors in parallel is given by,

CALCULATION:

Given C1 = C2 = C3 = C4 = C5 = C 

  • When they are connected in series the equivalent capacitance is given as,

     -----(1)

  • When they are connected in parallel the equivalent capacitance is given as,

    ----- (2)

By dividing equation 1 and equation 2,

  • Hence, option 3 is correct.

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