The capacitance of a parallel plate capacitor is C. The capacitance of the capacitor, if a metal foil of negligible thickness is introduced parallel to the plates at its centre, will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → C
The foil divides the gap into two capacitors in series, each with plate separation d/2. A conducting sheet of negligible thickness does not reduce the total gap between the plates.
\( \displaystyle C = \frac{\varepsilon_0 A}{d} \)
\( \displaystyle C_1 = C_2 = \frac{\varepsilon_0 A}{d/2} = 2C \)
\( \displaystyle \frac{1}{C'} = \frac{1}{2C} + \frac{1}{2C} = \frac{1}{C} \)
\( \displaystyle C' = C \)
Note: A similar question was also asked in CUET (UG) 2023 on 11-06-2023 (Slot 3) and on 07-06-2023 (Slot 3).