Two parallel air capacitors have their plate areas 100 ~cm ^2 and 500 ~cm ^2 , respectively. They have the same charge and potential. If the distance between the plates of the first capacitor is 0.5 ~mm , the distance between the plates of the second capacitor is

Step-by-step solution

Here, two parallel plate capacitors have same charge q and same potential V, so they have equal capacitances as aligned & C = q V & C ₁= C ₂ & ₀ ~A ₁ ~d ₁ = ₀ ~A ₂ ~d ₂ & Or d ₂= A ₂ ~A ₁ ~d ₁ & Now, A ₁=100 ~cm ^2, ~A ₂=500 ~cm ^2 & ~d ₁=0.5 ~mm =0.05 ~cm & d ₂= 500 0.05 100 =0.25 ~cm =2.5 ~mm aligned