A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance $\mathrm { C } _ { 0 }$. Now one-third of the material is replaced by another material with dielectric constant 2K, so that effectively there are two capacitors one with area $\frac { 1 } { 3 } \mathrm {~A}$, dielectric constant 2K and another with area $\frac { 2 } { 3 } \mathrm {~A}$ and dielectric constant K. If the capacitance of this new capacitor is C then $\frac { \mathrm { C } } { \mathrm { C } _ { 0 } }$ is (1) 1 (2) $\frac { 4 } { 3 }$ (3) $\frac { 2 } { 3 }$ (4) $\frac { 1 } { 3 }$
A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance $\mathrm { C } _ { 0 }$. Now one-third of the material is replaced by another material with dielectric constant 2K, so that effectively there are two capacitors one with area $\frac { 1 } { 3 } \mathrm {~A}$, dielectric constant 2K and another with area $\frac { 2 } { 3 } \mathrm {~A}$ and dielectric constant K. If the capacitance of this new capacitor is C then $\frac { \mathrm { C } } { \mathrm { C } _ { 0 } }$ is\\
(1) 1\\
(2) $\frac { 4 } { 3 }$\\
(3) $\frac { 2 } { 3 }$\\
(4) $\frac { 1 } { 3 }$