GATE 2026 IN – Question 50
A parallel-plate capacitive displacement sensor has a plate area of $2\ \mathrm{cm^2}$. The air gap between the plates is decreased by 0.1 mm from an initial value of 0.5 mm. The percentage change in the capacitance value is ________ %. Assume the permittivity is $\varepsilon_0=8.854\times10^{-12}\ \mathrm{F/m}$.
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Correct answer: (C) 25.0
Explanation
For fixed area and permittivity, $C=\varepsilon A/d$. The final gap is $d_2=0.5-0.1=0.4\ \mathrm{mm}$, so $C_2/C_1=d_1/d_2=0.5/0.4=1.25$.
The percentage increase is $(1.25-1)\times100=25\%$. Thus the answer is **25.0% (C)**. The supplied area and permittivity cancel in this ratio.