Rows of capacitors containing 1, 2, 4, 8, ……., `oo` capacitors, each of capacitance 2F, are connected in parallel as shown in figure. The potential difference across AB is 10 V, then

Options

A. total capacitance across AB is 4F
B. charge on each capacitor will be same
C. charge on the capacitor in the first row is more than on any other capacitor
D. energy of all the capacitors is 50 J.

Answer

A, C

Explanation

a.,c.
Capacities in different arms are
`2F,1F,(1)/(2)F,(1)/(4)F,`....
`C_(eff)=2+1+(1)/(2)+(1)/(4)+....oo=2(1+(1)/(2)+(1)/(4)+...)=4F`.
As `PD` across each row is same, thus the charge will be maximum across the cpacitor in first now