Two parallel plate capacitors, each of the capacitance \( 40\,\mu\mathrm{F} \) are connected in series. The space between the plates of one capacitor is filled with a material of dielectric constant \( K = 4 \). The equivalent capacitance of the system would be :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 32\,\mu\mathrm{F} \)
Filling a capacitor completely with a dielectric multiplies its capacitance by \( K \).
\( C_1 = 40\,\mu\mathrm{F} \)
\( C_2 = K C = 4 \times 40 = 160\,\mu\mathrm{F} \)
For capacitors in series,
\( \displaystyle C_{\mathrm{eq}} = \frac{C_1 C_2}{C_1 + C_2} = \frac{40 \times 160}{40 + 160}\,\mu\mathrm{F} = \frac{6400}{200}\,\mu\mathrm{F} = 32\,\mu\mathrm{F} \)
Note: A similar question was also asked in CUET (UG) 2026 on 31-05-2026 (Slot 2).