AIIMS 2001 Physics Capacitors with Dielectrics MCQ Question

To find the capacitance of a capacitor with two dielectric materials, we can use the formula for capacitors in series. The equivalent capacitance for two dielectrics with dielectric constants K₁ and K₂ is given by: $C = \frac{\varepsilon_0 A}{d} \cdot \frac{K_1 K_2}{K_1 + K_2}$ where A is the area of the plates and d is the separation between them. In this case, the correct answer is B) $C = \varepsilon_0 A \frac{K_1 K_2}{K_1 + K_2}$ because it correctly represents the capacitance in terms of the dielectric constants of the two materials.

Option A) is incorrect because it suggests an average of the dielectric constants rather than their product divided by their sum.

Option C) is incorrect because it implies a direct ratio of the dielectric constants without considering the geometry of the capacitor.

Option D) is incorrect as it incorrectly multiplies the dielectrics and divides by their sum, which does not apply to the series configuration of capacitors. Thus, the correct answer is B.