Question

Diagram shows three arrangements of dielectric in a capacitor. Arrange the capacitors in increasing order of capacitance between A and B if $K_1>K_2$. 

• A. $C_A<C_B<C_C$
• B. $C_A<C_C<C_B$
• C. $C_B<C_C<C_A$
• D. $C_B<C_A<C_C$

Hint:

Dielectric closer to regions of stronger electric field contributes more to increasing capacitance.

Answer 1

The Correct Option is C

Step 1: Basic principle of capacitance

Capacitance depends on how effectively the electric field between the plates is reduced. A dielectric with higher dielectric constant reduces the electric field more and hence increases capacitance.

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Step 2: Analysis of arrangement C_A

In arrangement C_A, the dielectric with higher dielectric constant K₁ occupies the region where the electric field is strongest.

This results in maximum reduction of electric field and hence maximum capacitance.

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Step 3: Analysis of arrangement C_B

In arrangement C_B, the dielectric with lower dielectric constant K₂ dominates the effective region between the plates.

Since K₂ < K₁, the reduction in electric field is minimum, giving the least capacitance.

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Step 4: Analysis of arrangement C_C

In arrangement C_C, both dielectrics share the field region almost equally.

Therefore, the effective dielectric constant lies between K₁ and K₂, resulting in intermediate capacitance.

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Step 5: Final comparison

Since K₁ > K₂, the capacitances follow the order:

C_B < C_C < C_A