According to relation $V$ equals $\frac{W}{Q}$ , $4V$ is inversely proportional to $Q$ but according to relation $Q$ equals to $CV$ potential is directly proportional to charge, what is the difference between these two cases?
[Physics] the relation between potential and charge
capacitancechargeelectrostaticspotential
Related Solutions
then why is there no potential difference between the two capacitors
It's not quite clear what you mean here but do understand that charged capacitors are electrically neutral.
When a capacitor is "charged", it is not electrically charged, it is energy charged in the same sense as when we say a battery is charged.
There is nothing mysterious about two series connected circuit elements having different voltage drops. Think of two series connected resistors with different resistor values.
I would have thought that as plate B is positively charged and plate C is negatively charged, there would be a potential difference between the two
You're forgetting something fundamental: The plates B and C along with the wire that connects them are conductors. But, for an ideal conductor, charge distributes itself so that there is no (static) potential difference across the conductor.
The voltage between the bottom plate of C1 and the top plate of C2 is zero precisely because a conductor connects the two plates.
What is Electric Potential?
Electric potential (V) is the property of points in space. Electric potential can be defined in several ways:
The value of the electric potential at a point in space numerically gives the amount of work that needs to be done to bring a unit positive charge from infinity to that point.
A charge $q$ is said to have a potential energy of $Vq$ if it is at a point in space which has a potential of $V$.
For example, if you place a charge $q$ at a point, space nearby will have a non-zero value of potential. The electric potential at a point due to a charge at a distance $r$ from it is given by:
$$V = \frac{kq}{r}$$
What is Electric Potential Energy?
Electric potential energy (U) is the property of a system. Two charges in the vicinity of each other are said to have potential energy.
The electric potential energy associated with two charges separated by a distance $r$ is given by: $$U = \frac{kq_1q_2}{r}$$
Best Answer
These two equations describe completely different things.
$V = W/Q$ says that if you have a test charge $Q$, and you want to move it from place-1 to place-2, and it takes an amount of work $W$ to do it, then the potential (voltage) at place-2 is higher than that at place-1 by an amount $V$. The equation may make it may look like $V$ depends on $Q$, but it does not: if you double the charge, it takes twice as much work to move it, and the $V$ remains the same. The potential is a function of the pre-existing electric field, and the equation simply tells you how much work it takes to move a given amount of charge around in that field.
$Q=CV$ says that the potential difference across a capacitor is proportional to the amount of charge on each plate of the capacitor, and defines the capacitance, $C$ as the constant of proportionality. It is much less general than the first equation: there are many situations where the concept of capacitance is not applicable. Moreover, the charge referred to in the equation is the charge that produces the field, not one that experiences it.