51. It is A/d-t

d = .005m and t = .004m and k is infinite as it is a metal slab.

8.85 x 10^-12 x 100 x 10^-4 / .001 = 88 pF

 

52. Here u should remember one thing that as long as the battery remains connected the potential must remain consta.

 

So we got V = Const.

OR Q  Capacitance (as Q=VC)

i.e. if Q increases then C increaes

 

As in the question it is given that 100 C charge flows through the battery then this 100 C charge will be extra on capacitor which it has drawn from battery.

 

So new net charge is 50 + 100 = 150 C

Then why the charge increased ??? It is due to increase in capacitance of the capacitor due to insertion of dielectric.

 

Now the problem is quite simple

Just take the ratios of K = 150/50 = 3

C_new/C = Q₁₅₀/Q₅₀

And Cnew is KA/d