Case: Read the passage and answer the question.
A capacitor is a system of two conductors separated by an insulator. The electric field in the region between the conductors is proportional to the charge Q. That is, if the charge on the capacitor is, say, doubled, the electric field will also be doubled at every point. A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance. Dielectrics are introduced between the plates to change the nature of capacitors. Capacitors can be connected in series and in parallel in a circuit.
What is the effective capacitance C when two capacitors \( C_1 \) and \( C_2 \) are connected in parallel?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( C=C_1+C_2 \)
In a parallel combination both capacitors are connected across the same two points. So they have the same potential difference V, but their charges can differ.
Option (1) \( C=C_1+C_2 \) — Correct. The equivalent capacitor holds the total charge \( Q=C_1V+C_2V \) at the same V, so with \( Q=CV \) the capacitances add.
Option (2) \( \displaystyle\frac{1}{C}=C_1+C_2 \) — Incorrect. The left side has the unit F−1 and the right side F, so this relation is not even dimensionally correct.
Option (3) \( \displaystyle\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2} \) — Incorrect. This is the series combination, in which both capacitors carry the same charge and their potential differences add.
NCERT (2026-27):
Capacitors in Parallel – “… In this case, the same potential difference is applied across both the capacitors. …
\( Q=CV=C_1V+C_2V \qquad (2.63) \)
The effective capacitance C is, from Eq. (2.63),
\( C=C_1+C_2 \)\( \qquad (2.64) \)”