GATE EE 2025 Set 1 — Question 50
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Electromagnetic Fields → Electrostatics → Capacitance
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Question
An air filled cylindrical capacitor (capacitance ) of length , with and as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a dielectric material of relative permittivity is inserted inside 50% of the annular region as shown in Fig. (ii). The value of for which the capacitance of the capacitor in Fig. (ii), becomes is
Correct answer
(C) 9
Solution
Capacitance of an air-filled cylindrical capacitor is . In Fig (ii), the dielectric is inserted in 50% of the annular region (half the circumference). This forms two capacitors in parallel: (air part) and (dielectric part). Total capacitance . Given , we have .
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