question_answer

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor

A) Decreases          

B) Remains unchanged

C) Becomes infinite

D) Increases

Correct Answer: B

Solution :

[b] The capacitance of the capacitor with air as dielectric is given by \[C=\frac{{{\varepsilon }_{0}}A}{d},\] Where A is the area of each plate and d is the distance between them. The capacitance of the capacitor with a conducting shell of thickness t is given by \[C=\frac{{{\varepsilon }_{0}}A}{d-t},\] Now, if\[t\to 0\], then \[C={{\varepsilon }_{0}}A/d\] Therefore, when a sheet of aluminium foil of negligible thickness is introduced between the plates of the capacitor, its capacitance remains unchanged.