Question

Determine a formula for the capacitance in terms of K1 , K2 , the area A of the plates, and the separation d . [Hint: Can you consider this capacitor as two capacitors in series or in parallel

Answer 1

Based on the capacitance of both capacitors, the formula in terms of K1, K2, and the area is (2 x ε₀ x A x K₁ x K₂) / (d x (K₁ + K₂)).

What is the formula for the capacitance?

Express the capacitance of the first capacitor as:

C₁ = (k₁ x ε₀ x A) / d₁

Express that of the second capacitor as:

C₂ = (k₂ x ε₀ x A) / d₂

The equivalence capacitance will be:

1/C = ( d₁ / (k₁ x ε₀ x A)) + (d₂ / (k₂ x ε₀ x A))

C = (2 x ε₀ x A x K₁ x K₂) / (d x (K₁ + K₂))

Full question is:

Two different dielectrics fill the space between the plates of a parallel-plate capacitor as shown in Fig. 24-31. Determine a formula for the capacitance in terms of K1, K2, the area A, of the plates, and the separation d1 = d2 = d/2. [Hint: Can you consider this capacitor as two capacitors in series or in parallel?]

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