When an additional charge 2C is given to a capacitor, energy stored in it is increased by 21%. The original charge of the capacitor is

Options

A. 30 C
B. 40 C
C. 10 C
D. 20 C

Answer

D

Explanation

Let Q C be original charge of the capacitor and C be capacitance of the capacitor.
`:.` Initial energy stored in the capacitor is
`u= (1)/(2) (Q^(2))/(C )`..(i)
When an additional charge of 2C is given to a capacitor, its charge on the capacitor becomes
`Q' = Q +2`...(ii)
Now energy stored in the capacitor is
`u' = (1)/(2) (Q'^(2))/(C )` ...(iii)
As per question
`u' = u + (21)/(100) u = (121)/(100)u`
`:. (1)/(2) (Q'^(2))/(C ) = (121)/(100) ((1)/(2) (Q^(2))/(C ))` (Using (i) and (iii))
`Q'^(2) = (121)/(100) Q^(2) or Q' = (11)/(10)Q`
`Q + 2 = (11)/(10)Q` (Using (ii))
`10(Q + 2) = 11Q`
`10Q + 20 = 11Q or Q= 20C`