Question

In the figure shown, find the capacitance between points $\text{A}$ and $\text{B}$, if the area of each plate is $A$ and separation between the adjacent plates is $d$.

• A. $\frac{{ϵ}_{0}A}{d}$
• B. $\frac{3{ϵ}_{0}A}{d}$
• C. $\frac{2{ϵ}_{0}A}{d}$
• D. $\frac{{ϵ}_{0}A}{2d}$

Answer 1

The correct option is A $\frac{{ϵ}_{0}A}{d}$



Assuming potential at point $\text{A}=V_A$ and potential at $\text{B}=V_B$

There are $3$ capacitors formed, as we can observe from the figure.

And potential difference $\Delta V$ across $1$ is

$\Delta V_1=V_B-V_B=0$

Similarly,

$\Delta V_2=V_A-V_B;\Delta V_3=V_A-V_A=0$

So effectively there is only one capacitor to be considered between points $\text{A}$ and $\text{B}$ which is $2$.

$\therefore C_{AB}=\frac{{ϵ}_{0}A}{d}$

Therefore, the correct option is $\left(A\right)$.