Question

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. All the geometric parameters of the capacitor (plate diameter and plate separation) are now DOUBLED. If the original capacitance was Co, what is the new capacitance? Select one: a. Co/4 b. 4C0 c. Co/2 d. Co e. 2Co

Answer 1

Capacitance of a air filled parallel plate capacitor is $C = \frac{A\epsilon_{o}}{d}$ [ A = area of plates , d = separation between the plates ]

now,

let the radius of circular plate used be R, separation be d, then initial capacitance is

to C. d

Now, the R and d is doubled then new capacitance is C = $C = \frac{\pi (2R)^{2}\epsilon_{o}}{2d} = \frac{2\pi R^{2}\epsilon_{o}}{d} =2C_{o}$ [correct option is option e]