Capacitance: Introduction and calculation

1. Introduction

  • A capacitor (formerly known as condenser) is a device that can store electronic charge and energy.
  • All capacitors consists of a combination of two conductors separated by an insulator.
  • The insulator is called dielectric which could be oil, air or paper and many more such materials are there wich can act as a dielectric medium between conducting plates of a capacitor.
  • Figure 1 below shows the symbol used to represent a capacitor.

    Figure below shows the symbol used to represent a capacitor

  • Now plates of the capacitor are connected to the terminals of a battery, shown below in figure 2, in order to charge it's conducting plates.

    plates of the capacitor are connected to the terminals of a battery

  • As soon as capacitor is connected to the battery , charge is transferred from one conductor to another.
  • Plate connected to positive terminal of the battery becomes positively charged with charge +Q in it and plate connected to negative terminal of the battery becomes negatively charged with cahrge -Q on it i.e. both plates have equal amount of opposite charge .
  • Once the capacitor is fully charged potential difference between the conductors due to their equal and opposite charges becomes equal to the potential difference between the battery terminals.
  • For a given capacitor Q∝V and the ratio Q/V is constant for a capacitor.
              Q=CV                              (1)
    where the proportionality constant C is called the capacitance of the capacitor.
  • Capacitance of any capacitor depends on shape , size and geometrical arrangement of the conductors.
  • When Q is in coulumbs (C) and V is in volts(V) then the S.I. unit of capacitance is in farads(F) where
              1F=1 coulumb/volt
  • One farad is the capacitance of very large capacitor and it's submultiples such as microfarad(1μF=10-6) or picofarad(1pF=10-12) are generally used for practical applications.

2. Calculation of capacitance

  • For calculating capacitance of a capacitor first we need to find the potential difference between it's two conducting plates having charge +Q and -Q.
  • For simple arrangements of conductors like two equivalent parallel plates kept at distance d apart or two concentric conducting spheres etc., potential difference can be found first by calculating electric field from gauss's law or by Coulumb's law.                     
  • After calculating electric field , potential difference can be found by integrating ellectric field using the relation
    where the limits of integration goes from a to b.
  • Once we know the potential difference between two conductors of the capacitor , it's capacitance can be calculated from the relation
              C=Q/V                              (2)
  • Calculation of capacitance of some simple arrangements would be illustrated in following few articles.

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Class 12 Maths Class 12 Physics

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