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. 10 second
B. 5 second
C. 2.5 second
D. 20 second

Answer

C

Explanation

Time constant for parallel combination = 2RC
Time constant for series combination =` (RC)/(2)`
In first case :
`V = V_(0)e^(t_(1))/(2RC) = (V_(0))/(2)` " ...(1)
In second case :
`V = V_(0)e^((-t_(2))/(RC/2)) = (V_(0))/(2)` " ...(2)
From (1) and (2)
`(t_(1))/(2RC) = (t_(2))/((RC)/(2)) Rightarrow t_(2) = (t_(1))/(4) = (10)/(4) = 2.5 sec.`