question_answer

A thin aluminium sheet is placed between the plates of a parallel plate capacitor. Its capacitance will:

A) increase                              

B)  decrease

C) remain same                     

D) become infinite

Correct Answer: C

Solution :

Key Idea: On inserting a thin aluminium sheet between the plates of a capacitor it act as two capacitors connected in series. The combination shows two capacitor connected in series. Resultant capacitance is \[\frac{1}{C'}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}\] \[C=\frac{K{{\varepsilon }_{0}}A}{d}\] where, A is area, d is the distance between the plates and K is dielectric constant (=1). Therefore,  \[{{C}_{1}}=\frac{{{\varepsilon }_{0}}A}{d/2},{{C}_{2}}=\frac{{{\varepsilon }_{0}}A}{d/2}\] \[\therefore \]                \[\frac{1}{C'}=\frac{d/2}{{{\varepsilon }_{0}}A}+\frac{d/2}{{{\varepsilon }_{0}}A}\] \[\frac{1}{C'}=\frac{d}{{{\varepsilon }_{0}}A}\] \[\Rightarrow \]               \[C'=\frac{{{\varepsilon }_{0}}A}{d}=C\] Hence, on inserting aluminium sheet the capacitance remains the same.