Question

A parallel-plate capacitor has a capacitance of C₁ Farads. Initially, it has a vacuum between the plates. Then, the space between the plates is completely filled with a plastic that has a dielectric constant K. A second capacitor with capacitance C₂ is then connected in series with the first capacitor, reducing the total capacitance back to C₁ . What is C₂ in terms of K,C₁, and relevant constants?

Answer 1

To find C₂, the capacitance of the second capacitor, use the formula 1/C₁ = 1/(KC₁) + 1/C₂, where K is the dielectric constant and C₁ is the original capacitance of the first capacitor. Solving for C₂ gives C₂ = C₁(K - 1)/K.

Step-by-step explanation:

The student is inquiring about the situation where a parallel-plate capacitor with capacitance C₁ initially has a vacuum between the plates, and then its capacitance changes once it's filled with a dielectric material of dielectric constant K. When another capacitor with capacitance C₂ is connected in series, the combined system's capacitance returns to C₁. The formula for capacitance in series is 1/C₁ = 1/(KC₁) + 1/C₂, and solving for C₂ yields C₂ = C₁(K - 1)/K.