X number of identical capacitors are connected in series and then in parallel. Then the ratio of the capacitances in parallel and series arrangement is-

The correct answer is option 2) i.e. X2

CONCEPT:​

• Capacitor: A capacitor is an electrical component with two terminals used to store charge in the form of an electrostatic field. 
  • It consists of two parallel plates each possessing equal and opposite charges, separated by a dielectric constant.
  • Capacitance is the ability of a capacitor to store charge in it. The capacitance C is related to the charge Q and voltage V across them as:

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• Equivalent capacitance of capacitors -
  • Connected in series: When n capacitors C1, C2, C3, ... Cn are connected in series, the net capacitance (Cs) is given by:

• Connected in parallel: When n capacitors C1, C2, C3, ... Cn are connected in parallel, the net capacitance (Cp) is given by:

⇒ Cp = C1 + C2  + C3 +...  Cn

EXPLANATION:

• Let C be the capacitance of each capacitor.

• When identical capacitors are connected in series, the equivalent capacitance, Cs 

Thus, the equivalent capacitance in series, C_s = C/X

• When the same capacitors are connected in parallel, the equivalent capacitance, Cp = C1 + C2  + C3 +...  Cn = XC

Thus, the equivalent capacitance in parallel, Cp = XC

Ratio =