Question

Consider the figure. Each capacitor has capacitance C.
The equivalent capacitance between 4 and 5 is

• A. $\left(\frac{3C}{4}\right)$
• B. $\left(\frac{3C}{2}\right)$
• C. $\left(\frac{3C}{5}\right)$
• D. $\left(\frac{5C}{4}\right)$

Answer 1

The correct option is B $\left(\frac{3C}{2}\right)$

As we need to find the equivalent capacitence between points 4 and 5 so, let us first connect these points to a power source or battery.Now from the figure we can see that three points (1, 2, 3) are at equal potential or they are bisymmetric points.
Since these are equi-potential points let us denote potential at these points as $x$.
Now, in between equi-potential points we know that there is no transfer of charges so we can simply elminate capacitors between points (1,2); (2,3) and (1;3).
Now the only potential points in the circuit are 4,$x$ and 5.
The simpler circuit diagram of this can be shown now as

​​​​​ The equivalent capacitance between point 4 and 5 will be
$\frac{1}{C_{eq}}=\frac{1}{3C}+\frac{1}{3C}$
$⟹$ $C_{eq}$ = $\frac{3C}{2}$