A condenser in series with a resistor is connected through a switch to a battery of negligible internal resistance and having an emf of `12 V`. One second after closing the switch, the condenser is found to have a potential difference of `6V`. The time constant of the system is

Options

A. `2 s`
B. `(1)/(log_(e) 2)`
C. `log_(e)2`
D. `log_(e) ((1)/(2))`

Answer

B

Explanation

`q = q_(0)(1-e^(-t//Rc))`, `t = 1 "second"`
`CV = CV_(0)(1-e^(-t//Rc)), (1)/(2) = e^(-t//Rc)`
`ln 2 = (1)/(Rc)lne , RC = (1)/(ln 2)`