There are six parallel plates of equal area A arranged as shown in figure (d

Question

There are six parallel plates of equal area A arranged as shown in figure (d < < A) . The equivalent capacitance between points 2 and 5 is α (ϵ 0 A/ d) . Then, find the value of α . <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-5w6hegbtiwdutjhl.jpg" /> (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Recall the feature of balanced meter bridge.
Solution

The above combination of capacitance is the example of a balanced meter bridge,

C_{A B} = C

.
Recall the formula of capacitance in terms of cross-sectional area and separation between the capacitors,

C = \frac{ϵ _{0} A}{d} = α \frac{ϵ _{0} A}{d}

α = 1

.

Q. There are six parallel plates of equal area A arranged as shown in figure (d<<A) . The equivalent capacitance between points 2 and 5 is αdϵ0​A​ . Then, find the value of α .

Recall the feature of balanced meter bridge. The above combination of capacitance is the example of a balanced meter bridge, CAB​=C . Recall the formula of capacitance in terms of cross-sectional area and separation between the capacitors, C=dϵ0​A​=αdϵ0​A​ α=1 .

Q. There are six parallel plates of equal area $A$ arranged as shown in figure $(d << A)$ . The equivalent capacitance between points $2$ and $5$ is $α \frac{ϵ _{0} A}{d}$ . Then, find the value of $α$ .