Question

Each capacitor in FIGURE CP26.83 has capacitance $C$. What is the equivalent capacitance between points $a$and $b$?

Short answer

The equivalent capacitance between points$a$and$b$is$2C.$

Step-by-step solution

Concept Introduction

In a circuit, equivalent capacitance refers to the sum of the capacitance of all the capacitors connected together. There are two modes of connecting capacitors together.

Explanation

By identifying the capacitors by numbers, the top one would be 1, followed by 2 and 3, followed by 4,5, and 6.

It is connected in series with capacitors 1 and 6 and together with capacitors 2 and 5 and with capacitors a, b;

It is connected in series with capacitors 1 and 6 and together with capacitors a, b;

The third capacitor is connected in series between the two systems described above. But here's the catch: this capacitor is useless!

Due to the fact that all the capacitors (even 1 and 2 combined, and 5 and 6 together) have the same capacitance, there will be no potential difference applied to capacitor 3; therefore, it has no impact on the scheme;

Capacitor 4 is connected in parallel to the two systems.

Considering the following, each system in series will have a capacitance of $\frac{C}{2}$.

Since the two systems are connected in parallel, we will have a capacitance of $\frac{C}{2}+\frac{C}{2}=C$for our system of four capacitors $(1,2,5,6)$.

Connecting this in parallel with the $C$provided by capacitor 4 yields a total of,

$C_{eq}=2C.$

Final Answer 

Hence, the equivalent capacitance between points$a$and$b$is$2C.$