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An air filled cylindrical capacitor (capacitance 
) of length 
, with 
and 
as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a dielectric material of relative permittivity 
is inserted inside 
of the annular region as shown in Fig. (ii). The value of for which the capacitance of the capacitor in Fig. (ii), becomes 
is
4
5
9
10
It is given that 
Since half of the region is filled with air and half with a dielectric the two parts can be considered to be connected in parallel and the capacitance is equally divided as 
Option (c) is contest.