question_answer

Seven identical plates, each of area A, are placed as shown. Any two adjacent plates are at separation d. Conducting wires have been used to connect the plates and a cell of emf V volt as shown in the figure. How much charge does the cell supply?

A) \[\left( \frac{{{\varepsilon }_{0}}A}{d} \right)V\]             

B) \[\left( \frac{{{\varepsilon }_{0}}A}{2d} \right)V\]

C) \[\left( \frac{2{{\varepsilon }_{0}}A}{2d} \right)V\]                      

D) \[\left( \frac{{{\varepsilon }_{0}}A}{4d} \right)V\]

Correct Answer: A

Solution :

[a] There are five capacitors each of capacitance \[C=\frac{{{\varepsilon }_{0}}A}{d}\]. The arrangement is a Wheatstone bridge as shown in figure.

It is a balanced bridge and equivalent capacitance is \[{{C}_{0}}=C=\frac{{{\varepsilon }_{0}}A}{d}\] \[Q={{C}_{0}}V=\frac{{{\varepsilon }_{0}}A}{d}V\]