A parallel plate air capacitor has a capacity of 2 pF. If the separation between its plates is doubled and a mica sheet is introduced between its plates, Its capicity becomes 6 pF. What Is the dielectric constant of mica?
Correct answer: A. 6
- A. 6
- B. 5
- C. 4
- D. 3
Explanation
The capacitance of a parallel plate capacitor is given by the formula C = ε₀ * (A/d), where ε₀ is the permittivity of free space, A is the area of the plates, and d is the separation between the plates. When a dielectric material with a dielectric constant κ is introduced, the capacitance becomes C' = κ * ε₀ * (A/d'). If the separation d is doubled, the new capacitance with the dielectric is given as 6 pF. Solving for κ with the given changes, we find that κ = 6. Thus, the dielectric constant of mica is 6. Options B, C, and D result in capacitances that do not match the given conditions when similarly calculated, confirming they are incorrect.
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