Class 10 > Unit # 14: Electrostatics > Capacitor and Capacitance

Talha's Physics Academy

Electrostatics - Capacitance and Capacitors

Q. Define capacitance and capacitors and write the factors on which capacitance of a capacitor depends.

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Figure: Parallel plate capacitor storing electric charges across insulating dielectric media.

Capacitance

The electric potential $V$ of an isolated conductor is directly proportional to its own charge $q$:

$q \propto V \implies q = C V$

Where $C$ represents the capacitance (capacity of holding electric charge), defined formally as:

"The charge stored per unit potential difference on a conductor is known as its capacitance."

$C = \frac{q}{V}$

The capacitance depends primarily on the physical size and geometric shape of the conductor.

Unit of Capacitance

The SI unit of capacitance is the Farad (F).

Definition: "If a charge of 1 coulomb given to a conductor raises its potential difference by 1 volt, then its capacitance is equal to 1 Farad ($1 \, \text{F} = 1 \, \text{C}/1 \, \text{V}$). Note that the Farad is a very large unit in practical applications, so microfarads ($\mu\text{F}$) or picofarads ($\text{pF}$) are commonly used."

Capacitor

"A capacitor is a passive electronic device designed to store electric charge and electrical energy in an electrostatic field. It typically consists of two parallel conducting plates separated by air or an insulating dielectric material, carrying equal and opposite charges."

Capacitors are engineered to store substantial amounts of electric charge without requiring excessively large physical dimensions.

Factors on which Capacitance Depends

The capacitance $C$ of a parallel plate capacitor is governed by three primary physical factors:

1. Area of the Plates ($A$):
   The capacitance increases directly as the surface area of the conducting plates increases.

   $C \propto A$
2. Distance Between the Plates ($d$):
   The capacitance increases as the separation distance between the plates decreases.

   $C \propto \frac{1}{d}$
3. Dielectric Medium / Constant ($\varepsilon_r$):
   Inserting an insulating dielectric medium with a high relative permittivity (dielectric constant $\varepsilon_r$) between the plates significantly enhances the capacitance.

   $C \propto \varepsilon_r$

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