The GATE Grind

GATE 2023 IN – Question 15

Electricity and Magnetism · Electrostatics and capacitance · 1 mark · Multiple choice

A parallel-plate capacitance is calculated as 20 pF using $C=\epsilon_0\epsilon_rA/d$, where $\epsilon_0$ is free-space permittivity, $\epsilon_r$ relative dielectric permittivity, $A$ overlapping electrode area, and $d$ electrode spacing. It is then measured with an ideal LCR meter, with no cable-capacitance error. Which reading is likely to be correct?

  1. 20.5 pF
  2. 20 pF
  3. 19.5 pF
  4. 10 pF

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Show answer and explanation

Correct answer: (A) 20.5 pF

Explanation

The simple εA/d formula neglects edge fringing. Fringing adds electric flux and slightly increases capacitance above the calculated 20 pF. Among the readings, **20.5 pF, A** is the plausible ideal-meter result.