question_answer

The given figure shows a sheet of aluminium foil of negligible thickness placed between the plates of a capacitor. Aluminium foil sheet

How will its capacitance be affected, if

(i) the foil is electrically insulated?

(ii) the foil is connected to the upper plate with a conducting wire?

Answer:

(i) The system will be equivalent to two identical capacitors connected in series combination in which two plates of each capacitor have separation half of the original separation. Thus, new capacitance of each capacitor \[C'=2C\]           \[\left[ \because \,\,\,C\propto \frac{1}{d} \right]\]             \[\because \]       \[C'\] and \[C'\]are in series             \[\Rightarrow \]   \[{{C}_{\text{net}}}=\frac{2C\times 2C}{2C+2C}=C\]                         \[{{C}_{\text{net}}}=C=\] original capacitor             (ii) System reduces to a capacitor whose separation reduces to half of original one.             \[\therefore \]      New capacitance, \[C'=2C\]