Question

The area of every plate shown in figure is A and the separation between the successive plates is d. What is the capacitance between points a & b. __________.

• A. $\frac{{\epsilon }_{0}A}{d}$
• B. $2\frac{{\epsilon }_{0}A}{d}$
• C. $3\frac{{\epsilon }_{0}A}{d}$
• D. $4\frac{{\epsilon }_{0}A}{d}$

Answer 1

The correct option is B $2\frac{{\epsilon }_{0}A}{d}$

Let us give numbers to the four plates.Here 1 and 2 are connected to the positive and negative terminals of the batery(figure 1).

Now, the arrangement can be represented as the grouping of two identical capacitors each of capacity $\frac{{ϵ}_{0}A}{d}$. The arrangement will be as shown (figure 2).

As we can see from the figure 2,these two capacitance are in parallel , so the equivalent capacitance between 1 and 2 is

$C_{12}$= (C+C) = 2C= $2\frac{{ϵ}_{0}A}{d}$.

Therefore, B is the correct option.