Question 274: Electrostatics & Capacitance

Question

A parallel plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K
1
and K
2
of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:
![](https://imagex.cdn.examgoal.net/1ktemfy4f/0a1f195f-5629-4861-b422-960998efe88a/d7bc20f0-125a-11ec-a4fb-5347f21481c0/file-1ktemfy4g.jpeg)

Accepted Answer

${C_{eq}} = {{{A \over 2}{\varepsilon _0}} \over d} + {{A{\varepsilon _0}} \over d}{{{K_1}{K_2}} \over {{K_1} + {K_2}}}$
$ = {{A{\varepsilon _0}} \over d}\left( {{1 \over 2} + {{{K_1}{K_2}} \over {{K_1} + {K_2}}}} \right)$
![](https://imagex.cdn.examgoal.net/1ktgvm78r/c111a083-2a46-429c-b2e4-5bd97de6737f/49189fb0-1398-11ec-bdf4-43280b6a7334/file-1ktgvm78s.jpeg)

Answer

${{{\varepsilon _0}A} \over d}\left( {{1 \over 2} + {{{K_1}{K_2}} \over {{K_1} + {K_2}}}} \right)$

Answer

${{{\varepsilon _0}A} \over d}\left( {{1 \over 2} + {{{K_1}{K_2}} \over {2({K_1} + {K_2})}}} \right)$

Answer

${{{\varepsilon _0}A} \over d}\left( {{1 \over 2} + {{{K_1} + {K_2}} \over {{K_1}{K_2}}}} \right)$

Answer

${{{\varepsilon _0}A} \over d}\left( {{1 \over 2} + {{2({K_1} + {K_2})} \over {{K_1}{K_2}}}} \right)$

Electrostatics & Capacitance

A parallel plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K 1 and K 2 of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:

Choose the correct answer: