Question

Find the capacitance between P and O. Each capacitor has capacitance $C$

• A. $2C$
• B. $3C$
• C. $8C$
• D. $6C$

Answer 1

The correct option is A $2C$

Let us first connect the points P and O to a power source or a battery.
Now, from the diagram we can analyse that some points in the circuit are symmetric about points P and O (i.e A, B, C and D). It means these are equi-potential points. We can denote these points by $x$.
So, we can remove all the capacitors lying in between these points If we carefully notice there are 4 capacitors lying in between points P and $x$ and further there are 4 capacitors lying in between $x$ and Q.
Let us now draw the schematic diagram of the capacitors connecting points P, $x$ and O.
The effective capacitance between points P and O will be
$\frac{1}{C_{eq}}=\frac{1}{4C}+\frac{1}{4C}$
$⟹C_{eq}=2C$