engineering recuitment BARC Stipendiary Trainee Category I 2023 Mock Test Physics Capacitance Capacitor with a Dielectric
A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K1 and K2 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 :
1
\(\frac{{{{\rm{\varepsilon }}_{\rm{0}}}{\rm{A}}}}{{\rm{d}}}\left( {\frac{1}{2}\, + \,\frac{{2\left( {{{\rm{K}}_{\rm{1}}}\, + \,{{\rm{K}}_{\rm{2}}}} \right)}}{{{{\rm{K}}_{\rm{1}}}{{\rm{K}}_{\rm{2}}}}}} \right)\)
2
\(\frac{{{{\rm{\varepsilon }}_{\rm{0}}}{\rm{A}}}}{{\rm{d}}}\left( {\frac{1}{2}\, + \,\frac{{{{\rm{K}}_{\rm{1}}}\,{{\rm{K}}_{\rm{2}}}}}{{2\left( {{{\rm{K}}_{\rm{1}}}\,{\rm{ + }}\,{{\rm{K}}_{\rm{2}}}} \right)}}} \right)\)
3
\(\frac{{{{\rm{\varepsilon }}_{\rm{0}}}{\rm{A}}}}{{\rm{d}}}\left( {\frac{1}{2}\, + \,\frac{{{{\rm{K}}_{\rm{1}}}\, + \,{{\rm{K}}_{\rm{2}}}}}{{{{\rm{K}}_{\rm{1}}}{{\rm{K}}_{\rm{2}}}}}} \right)\)
4
\(\frac{{{{\rm{\varepsilon }}_{\rm{0}}}{\rm{A}}}}{{\rm{d}}}\left( {\frac{1}{2}\, + \,\frac{{{{\rm{K}}_{\rm{1}}}\,{{\rm{K}}_{\rm{2}}}}}{{{{\rm{K}}_{\rm{1}}}\,{\rm{ + }}\,{{\rm{K}}_{\rm{2}}}}}} \right)\)