Question: Find the capacitance between P and O as shown in the figure. Each capacitor has capacitance C: A. ...

Question

Find the capacitance between P and O as shown in the figure. Each capacitor has capacitance C:
A. 2C
B. 3C
C. 8C
D. 6C

Answer 1

Solution

We know the formula for series and parallel combination of resistors. Opposite to that, we have a formula for series and parallel combination of capacitors. The formula of parallel combination of resistors is equal to the series combination of capacitors and the formula of series combination of resistors is equal to the parallel combination of capacitors. First, convert parallel loops into series then solve the series combination. To convert this first use the formula of parallel combination in PA and AO then use the formula of series combination.

Complete answer:

In the question, it is given that the capacitance of each capacitor is equal to C.
Capacitance is nothing but the ability of a conductor to store an electric charge and electrical potential energy is called capacitance.
Unit of capacitance is farad.
Calculations for capacitors are opposite to that of resistors.
As we can see in the figure four capacitors having capacitance C are connected in parallel in-between points P and A.
So the equivalent capacitance is given by parallel combination.
${{C}_{parallel}}=C+C+C+C=4C={{C}_{PA}}$
Similarly, the equivalent capacitance between points A and O is 4C.
Therefore, ${{C}_{PA}}={{C}_{AO}}=4C$
Now the circuit is compressed or converted in series combination.
So we can say that ${{C}_{PA}}$ and ${{C}_{AO}}$ are in series.
To find equivalent capacitance in series is,
${{C}_{PO}}=\dfrac{{{C}_{PA}}{{C}_{AO}}}{{{C}_{PA}}+{{C}_{AO}}}=\dfrac{4\times 4}{4+4}=2C$
So the capacitance between P and O is 2C.

Correct option is (A)

Note: In this question we don’t need to use the formula of capacitance equal to ratio of magnitude of charge and potential difference. It means we can also define capacitance as the ratio of magnitude of charge on either of conductors to the magnitude of potential difference between two conductors. Unit of capacitance is farad. There are two types of combination possible in capacitor: parallel and series. Series and parallel combination of capacitors has the opposite formula as that of resistance.