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Asked by Prashant DIGHE | 08 Mar, 2020, 09:40: PM
Expert Answer
Capacitance of parallel plate capacitor without any dielectric material,
[ εo A ] /d = [ εo π r2 ] / d = C ...................(1)
where εo is permittivity of free space, A is area of parallel plates, r is radius of plate and d is separation between plates
when space between parallel plate capacitor is partially filled with dielectric of radius r/2,
capacitor is divided into two parts, one with dielectric and remaining one without dielectric.
Both capacitors are connected in parallel.
Hence capacitance after the space is partially filled with dielectric is given by
{ [ εr εo π ( r2 / 4 ) ] / d } + { [ εo π ( r2 -( r2 / 4 ) ) ] / d } = Cnew .................(2)
where εr is dielectric constant that equals 6
Hence, eqn.(2) becomes, (3/2) { [ εo π r2 ] / d } + (3/4) { [ εo π r2 ] / d } = (9/4) { [ εo π r2 ] / d } = Cnew
Using eqn.(1), we get, Cnew = (9/4) C
Answered by Thiyagarajan K | 09 Mar, 2020, 12:36: AM
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