GATE EE 2018 Set 1 — Question 55
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Electromagnetic Fields → Electrostatics → Capacitance
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Question
The capacitance of an air-filled parallel-plate capacitor is pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _____________ (up to 2 decimal places).
Correct answer
2.5 to 2.55
Solution
Let the initial capacitance be pF.
When a dielectric slab of thickness and relative permittivity is inserted, the system acts as two capacitors in series: one with air () and one with the dielectric (). pF
pFThe equivalent capacitance is:
Given pF:
When a dielectric slab of thickness and relative permittivity is inserted, the system acts as two capacitors in series: one with air () and one with the dielectric (). pF
pFThe equivalent capacitance is:
Given pF:
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