Question

two parallel-plate capacitors are identical in every respect except that the separation of one is 1/2 the separation of the other. If the thinner capacitor has capacitance C, the larger one has capacitance _________ C.

Answer 1

If "d" is the distance between plates of a parallel plate capacitor and "A" is the area of cross section of plates then capacitance of this capacitor is given by

  

Now if the seperation between larger capacitor is d_l= d

then its capacitance is

Its given that seperation between thin capacitor is d_t= d/2

and Capacitance of thin capacitor is also given as "C" then we can write,

(Since both capacitors are identical hence will have same Area of Cross section)

or Capacitance of thin lens is (ANS)