Combination fo two identical capacitors, a resistor `R` and a dc voltage source of voltage `6V` is used in an experiment on a `(C-R)` circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combinatiomn reduces to half its original voltage is `10` second. For series combination the time needed for reducing teh voltage of the fully charged series combination by half is-

Options

A. 20s
B. 10s
C. 5s
D. 2.5s

Answer

D

Explanation

If `C_(e)` is the effective capacitance, then `V_(C)=(1)/(2)V_(0)`
`(q)/(C_(e))=(q_(0))/(2C_(e))`
As `q=q_(0)(1-e^((-t)/(RC_(e)))) implies q_(0)(1-C-t//RC_(e))=(q_(0))/(2) implies t=RC_(e)ln2`
For parallel grouping
`C_(e)=2C " "therefore t_(2)=2RCln2`
For series grouping
`C_(e)=(C)/(2)`
`therefore t_(1)=(RC)/(2)ln2 " "therefore (t_(2))/(t_(1))=(1)/(4)`.
`implies t_(2)=2.5` s