Match the Column I (parameter of capacitor) with Column II (value) and select the correct answer from the codes given below. Consider a dielectric inserted between the plates fully occupying the intervening region. The surface charge densities on the charged plates are 
.
Column I | Column II | ||
A. | Electric field E | I. | |
B. | Potential difference across the plates V | II. | |
C. | The capacitance C, with dielectric between the plates | III. | |
D. | Dielectric constant of the substance K | IV. |
Choose the correct answer from the option given below.
Text Solution
Verified by ExpertsD
The electric field in the dielectric corresponds to the case when the net surface charge density on the plates is 
, where 
surface charge density of dielectric.
… (i)
So the potential difference across the plates is
… (ii)
For linear dielectric, we except 
to be proportional to 
, i.e., to 
. Thus, ( 
) is proportional to 
and we can write
… (iii)
where, K is a constant characteristic of the dielectric. Clearly, 
, then we have
… (iv)
The capacitance C with dielectric between the plates is
… (v)
The product 
is called the permittivity of the medium and is denoted by 
.
… (vi)
For vacuum, 
and 
.
The dimensionless ratio, 
… (vii)
is called the dielectric constant of the substance. As remarked before, from Eq. (iii), it is clear that K is greater than 1.
From equations, 
and C 
K 
… (viii)
Hence, A-(II), B-(I), C-(IV), D-(III)
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