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Capacitor | Principle Of Capacitor

Capacitor | Principle Of Capacitor :- A capacitor is a device used to store a large amount of electric charge and electrical energy in a small space. In general, a capacitor consists of a pair of conductors carrying equal and opposite charges, separated by an insulating (dielectric) medium, which is capable of storing a definite amount of charge.

Principle Of Capacitor

The principle of a capacitor is based on the fact that the capacitance can be increased by reducing the potential while keeping the charge constant.

Suppose a conducting plate M is given a positive charge Q until its electric potential increases to the maximum value (V). If more charge is supplied beyond this, it will start leaking from the plate.

At this time, the capacitance of plate M,

$\displaystyle C=\frac{Q}{V}$

Now, as shown in the following figure, another identical conducting plate N is placed parallel to plate M in such a way that charge is induced on plate N.

Capacitor | Principle Of Capacitor - Curio Physics

If, due to the induced negative charge on plate N, the potential at plate M is V_–

, and due to the induced positive charge on plate N, the potential at plate M is V₊

, then the new value of the capacitance of plate M is,

$\displaystyle C'=\frac{Q}{V'}=\frac{Q}{V+{{V}_{+}}-{{V}_{-}}}$

Because V’ < V (compared to the positive induced charge, the negative induced charge is closer to plate M), therefore

⇒ C’ > C

Now, if the outer surface of plate N is grounded, then its entire positive charge will flow into the Earth.

Now, the potential difference between the plates M and N,

$\displaystyle {V}''=V-{{V}_{-}}$

The final value of the capacitance of plate M,

$\displaystyle C''=\frac{Q}{V''}=\frac{Q}{V-{{V}_{-}}}$

⇒ C” >> C

Therefore, if a uniform earthed conducting plate is placed near a charged conducting plate, the capacitance of the charged conductor increases. This is the principle of a parallel-plate capacitor.

A capacitor is an arrangement of two conductors separated by a dielectric medium, designed to store a large amount of electric charge and electrical energy in a small space.

If the conductors are parallel conducting plates, it is called a parallel plate capacitor; if they are spherical, it is called a spherical capacitor; and if they are cylindrical, it is called a cylindrical capacitor.

Curious Question

The principle of a capacitor states that the capacitance can be increased by reducing the potential while keeping the charge constant. However, we also say that the capacitance of a conductor does not depend on the charge given to it or on the potential; rather, it depends only on the geometrical configuration of the conductor (its size, shape, and separation) and on the surrounding medium.

Now the question is, if the capacitance increases when the potential is decreased, then why doesn’t capacitance depend on the potential?

Answer

The defining formula of capacitance is :

$\displaystyle C=\frac{Q}{V}$

This is the method to calculate capacitance, not an indication that C depends on V.

Capacitance is essentially a physical property that depends on :

Shape/Area of the plates
Distance between the plates
Nature of the medium (Dielectric constant K)

For example, the capacitance of a parallel plate capacitor is :

$\displaystyle C=K\frac{{{\varepsilon }_{0}}A}{d}$

Here you can see that it has neither Q nor V.

Then the question arises: “When we decrease the potential, the capacitance increases — so doesn’t this mean that capacitance depends on V?“

There is a very subtle point hidden here :

➡️ When you decrease the voltage and increase the capacitance, you keep Q constant. This means that you are changing the geometry or the medium of the capacitor.

Example :

If you insert a dielectric material between the two plates —

The dielectric reduces the potential
But you keep Q constant
Therefore, according to C = Q/V, the capacitance increases

➡️ This means that you actually changed the medium, rather than decreasing V ‘independently’.

Conclusion :

Capacitance does not depend on the voltage ; rather, it depends on the physical construction of the capacitor.
When we say that “capacitance increases by decreasing the potential”, it means that we have done something (such as inserting a dielectric or reducing the distance between plates) that caused to decrease while remained constant — resulting in an increase in capacitance.
However, this does not mean that depends on .

Mathematical example :

🔷 Condition 1 : Capacitor without dielectric material

Let’s say you have a parallel plate capacitor with the following characteristics :

No dielectric material ()

Capacitance :

$\displaystyle {{C}_{1}}=\frac{{{\varepsilon }_{0}}A}{d}=\frac{8.85\times {{10}^{-12}}\times 1}{{{10}^{-3}}}=8.85\times {{10}^{-9}}F$

Potential :

$\displaystyle {{V}_{1}}=\frac{Q}{{{C}_{1}}}=\frac{{{10}^{-6}}}{8.85\times {{10}^{-9}}}\approx 113V$

🔷 Condition 2 : Now, we insert a dielectric material between the plates

Now, let’s say you keep the capacitor as it is, but insert a dielectric material between the plates with a dielectric constant K = 5

New capacitance :

$\displaystyle {{C}_{2}}=K{{C}_{1}}=5\times 8.85\times {{10}^{-9}}=44.25\times {{10}^{-9}}F$

New potential :

$\displaystyle {{V}_{2}}=\frac{Q}{{{C}_{2}}}=\frac{{{10}^{-6}}}{44.25\times {{10}^{-9}}}\approx 22.6V$

🔶 Now understand this changes :

Change	Initially (no dielectric material)	Later (a dielectric material was inserted)
$Q$ (Charge)	10^-6C	Same
$C$ (Capacitance)	8.85 × 10⁻⁹F	Increased to
$V$ (Potential)	≈ 113 V	Decreased to

🔷 Conclusion :

You changed the medium by inserting a dielectric material → this is a physical change, which increased the capacitance.
The potential decreased, but that was the effect — not the cause.
Therefore, capacitance does not depend on the potential; rather, the potential changes due to the capacitance and charge

Capacitor | Principle Of Capacitor

Principle Of Capacitor

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