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GATE 2014 EE (EE1) – Question 17

Electromagnetic Fields · Effect of dielectric medium, Capacitance of simple configurations · 1 mark · Multiple choice

C₀ is the capacitance of the air-filled parallel-plate capacitor in (a). Half the gap, as shown in (b), is filled with relative permittivity ε_r. Find the modified capacitance.

Diagram for GATE 2014 EE (EE1) question 17
  1. $\frac{C_0}2(1+\epsilon_r)$
  2. $C_0+\epsilon_r$
  3. $\frac{C_0}2\epsilon_r$
  4. $C_0(1+\epsilon_r)$

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Show answer and explanation

Correct answer: (A) $\frac{C_0}2(1+\epsilon_r)$

Explanation

The drawing fills half the area across the full plate separation, creating parallel air and dielectric capacitors. Each has half the original area: Cair=C0/2and Cdielectric=εrC0/2. Add them to get **C=(C0/2)(1+εr),A**. A dielectric layer across half the thickness would require a series model instead.