GATE 2015 EE – Question 46

Electromagnetic Fields · Effect of dielectric medium, Capacitance of simple configurations · 2 marks · Numerical answer

A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm and 300 kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is ________.

Two plates 10 mm apart. The lower half of the gap, 5 mm, is glass with $\epsilon_r = 4.0$ and the upper 5 mm is air with $\epsilon_r = 1.0$.

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Correct answer: 17 to 20

Explanation

The flux density is continuous across the boundary, so $E_{glass} = \frac{E_{air}}{4}$. Air breaks down first, at $E_{air} = 30$ kV/cm $= 3$ kV/mm. Then $E_{glass} = 0.75$ kV/mm. The voltage is $3 \times 5 + 0.75 \times 5 = 18.75$ kV.