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: Understanding effect of dielectric arrangement.
Capacitance increases when dielectric with higher dielectric constant occupies a larger effective electric field region.
Step 2: Case $C_A$.
In $C_A$, dielectric $K_1$ occupies a larger effective region between plates, resulting in maximum capacitance.
Step 3: Case $C_B$.
In $C_B$, dielectric layers are arranged such that lower dielectric constant $K_2$ reduces the effective capacitance the most.
Step 4: Case $C_C$.
In $C_C$, the dielectrics are symmetrically arranged, giving capacitance between that of $C_A$ and $C_B$.
Step 5: Final comparison.
Since $K_1>K_2$, the increasing order of capacitance is:
\[ C_B<C_C<C_A \]