Question

If N capacitors of capacitance C each are connected in series, the equivalent capacitance is
1. C/N
2. CN
3. CN²
4. C³N

Answer 1

Correct Answer - Option 1 : C/N

The correct answer is option 1) i.e. C/N

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:

\(⇒ C =\frac{Q}{V} \)​

• 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:

\(⇒ \frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2}+ \frac{1}{C_3} + ... \frac{1}{C_n}\)

• 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:

When equal capacitors are connected in series, the equivalent capacitance, C_s \(⇒ \frac{1}{C_s} = \frac{1}{C} + \frac{1}{C}+ \frac{1}{C} + ... \frac{1}{C} =\frac{N}{C}\)

Therefore, equivalent capacitance C_s = C/N