A capacitor is a system of two conductors separated by an insulating medium. Capacitance of this system is determined purely geometrically, by the shapes, size and relative position of the conductors. The medium between the two conductors can be air or a dielectric. The way the dielectric is inserted accordingly by capacitance changes. Electric energy is stored in the capacitors. The capacitor can be connected in series or in parallel in an electric circuit.
Given below are two statements.
Statement I: Equivalent capacitance of a series combination of three capacitors will always be greater than any individual capacitance connected in series.
Statement II: When a series combination of three capacitors is connected across a voltage source, magnitude of charge stored on each plate of all the three capacitors is the same.
In the light of the above statements, choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Statement I is incorrect but statement II is true
In a series combination the reciprocals of the capacitances add, and the same charge flows onto every capacitor.
\( \displaystyle \frac{1}{C_{\mathrm{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \)
Statement I: Equivalent capacitance of a series combination of three capacitors will always be greater than any individual capacitance connected in series. — Incorrect. Since \( 1/C_{\mathrm{eq}} \) is greater than each \( 1/C_i \), \( C_{\mathrm{eq}} \) is smaller than the smallest individual capacitance, not greater.
Statement II: When a series combination of three capacitors is connected across a voltage source, magnitude of charge stored on each plate of all the three capacitors is the same. — Correct. In series there is a single path for the charge. The charge \( Q \) drawn from the source onto the first plate induces \( -Q \) on the facing plate, and the isolated conductor between two capacitors stays neutral, so every plate carries a charge of magnitude \( Q \).
NCERT (2026-27):
Capacitors in Series – “… Thus, in the series combination, charges on the two plates (±Q) are the same on each capacitor.”
Capacitors in Series – “… Following the same steps as for the case of two capacitors, we get the general formula for effective capacitance of a series combination of n capacitors:
\( \displaystyle \frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \ldots + \frac{1}{C_n} \qquad (2.60) \)”