Question

A parallel plate capacitor with 2 Air bern the plates has a Capaut arce C. What will be the Co pacitance if a) . The distance bets the plate , Pe doubled b. The space between the plates is filled with a d of electric constant. . ​

Answer 1

$\huge\mathcal\colorbox{lavender}{{\color{b}{SOLUTION:-}}}$

condition - 1 : d' = 2d

>> Let the distance between the plates be d'.

>> Let A be the area of each plate.

>> Capacitance of the parallel plate capacitor is given by:

$C = \frac{A∈ _{0}} { {d}^{ \: '} } \: . \: . \: . \: . \: .(1) \\ now \: {d}^{ \: '} = 2d \\ {d}^{ \: '} / 2=d\: . \: .\: . \: . \: .(given) \\ {C}^{'} = \frac{A∈ _{0}} {d} \\ \therefore {C}^{'} = \frac{A∈ _{0}} {d'/2} \\ \therefore{C}^{\: '} = \frac{C}{2} \: . \: . \: . \: . \: .(from-1)$

condition - 2 : filled with "k=5"

${C}^{''} = \frac{kA∈ _{0}} { {d}^{ \: '} } \\ {C}^{''} = kC \\ {C}^{''} = 5C\: . \: . \: . \: . \: .(from-1 \: and\: k=5)$