CBSE Class 12-science Answered
Define capacitance Derive an expression for capacitance of a parallel plate capacitor with dielectric
Asked by ap996969 | 23 Feb, 2019, 09:28: AM
Expert Answer
If two conductors , which are insulated from each other, are holding charges +Q and -Q respectively on their surfaces
and if the potential difference between them is V, Then the capacitance C of the system of these conductors is defined as C = Q/V
Parallel plate capacitor with dielectric
Let us assume, we have two large plates, each of area A, separated by a distance d. The charge on the plates is ±Q,
corresponding to the charge density ±σ (with σ = Q/A).
When there is vacuum between the plates, field E0 inside capacitor plates is given by, 
......................(1)
......................(1)Consider next a dielectric inserted between the plates fully occupying the intervening region. The dielectric is polarised by the field E0,
hece the effect is equivalent to two charged sheets (at the surfaces of the dielectric normal to the field) with surface charge
densities σp and –σp. The electric field in the dielectric then corresponds to the case when the net surface charge density on the
densities σp and –σp. The electric field in the dielectric then corresponds to the case when the net surface charge density on the
plates is ±(σ – σp).
That is, 
.............................(2)
.............................(2)so that the potential difference across the plates is 
...........................(3)
...........................(3)For linear dielectrics, we expect σp to be proportional to E0, i.e., to σ. Thus, (σ – σp) is proportional to σ and we can write
Thus, (σ – σp) is proportional to σ and we can write 
................................(4)
where K is a constant characteristic of the dielectric. Since K > 1 We then have
......................(5)
The capacitance C, with dielectric between the plates, is then
........................(6)
The product ε0K is called the permittivity of the medium and is denoted by ε
................................(4)where K is a constant characteristic of the dielectric. Since K > 1 We then have
......................(5)The capacitance C, with dielectric between the plates, is then
........................(6)The product ε0K is called the permittivity of the medium and is denoted by ε
Answered by Thiyagarajan K | 23 Feb, 2019, 12:56: PM
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