A capacitor of capacitance `100(mu)F` is charged by connecting it to a battery of emf 12 V and internal resistance `2(Omega)`. (a) Find the time constant of the circuit. (b) Find the time taken before 99% of maximum charge is stored on the capacitor.

Options

A. `0.92 ms `
B. `0.4 ms `
C. `0.8 ms`
D. `0.1 ms `

Answer

A

Explanation

During charging of capacitor, charge at any instant is
`q = q _(0) (1 - e ^( t // RC))`
`0.99 q _(0) = q _(0) (1 - e ^( -t//RC))`
`0.99 = (1- e ^( -t // RC))`
`0.01 = e ^(-t // RC)`
`e ^( t // RC) = 100`
`t = RC ln (100)`
`t (2) (100 xx 10 ^(-6)) (2 xx 2.303)`
`t = 0.92` ms