A) \[5{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]
B) \[15{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]
C) \[0.44\times {{10}^{-10}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]
D) \[8.845\times {{10}^{-11}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]
Correct Answer: C
Solution :
Capacitance of a parallel plate capacitor with air is\[C=\frac{{{\varepsilon }_{0}}A}{d}\]d Capacitance of a same parallel plate capacitor with the introductory of a dielectric medium \[C'=\frac{k{{\varepsilon }_{0}}A}{d}\]where k is the dielectric constant of a medium. \[\therefore \] \[\frac{C'}{C}=k\to =\frac{15}{3}=5\] and \[k=\frac{\varepsilon }{{{\varepsilon }_{0}}}\] or \[\varepsilon =k\,{{\varepsilon }_{0}}=5\times 8.854\times {{10}^{-12}}\] \[=0.4427\times {{10}^{-10}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]
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