Rankers Physics
Topic: Capacitors
Subtopic: Parallel Plate Capacitor

The capacitance of capacitor of plate areas A1 and A2 (A1 < A2) at a distance d is : Image related to
\[\frac{\varepsilon_{0}A_{1}}{d}\]
\[\frac{\varepsilon_{0}A_{2}}{d}\]
\[\frac{\varepsilon_{0}\left( A_{1}+A_{2} \right)}{2d}\]
\[\frac{\varepsilon_{0}\sqrt{A_{1}A_{2}}}{d}\]

Solution:

The capacitance of a parallel-plate capacitor is given by the general formula:

 

C=ε0AdC = \frac{\varepsilon_0 A}{d}

 

where:


  • CC
     

    = capacitance,


  • ε0\varepsilon_0
     

    = permittivity of free space,


  • AA
     

    = effective overlapping area of the two plates,


  • dd
     

    = separation between the plates.


For Plates of Unequal Areas ( A1<A2A_1 < A_2

 

):

When two plates of areas

A1A_1

and

A2A_2

are used to form a capacitor, only the smaller area (

A1A_1

) determines the effective overlapping area for charge storage. This is because the excess area of the larger plate (

A2A1A_2 - A_1

) does not contribute to the capacitance.

Thus, the capacitance is:

 

C=ε0A1dC = \frac{\varepsilon_0 A_1}{d}

 


Final Answer:

The capacitance of the capacitor is:

 

C=ε0A1d\boxed{C = \frac{\varepsilon_0 A_1}{d}}

 

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