Combination of 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 combination reduces to half its original voltage is `10` second. For series combination the time needed for reducing the 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

(c ) : RC circuit at DC supply
For parallel combination
C= 2C
Capacitor is discharging in time
`t_(1) =10 ` seconds .
The voltage drop
` V=V_(0)e(-(t_(1))/(RC))`
`V_(0)//2=V_(0)e(-(10)/(2RC))`

Again capacitors are connected in series the same amount of voltage is reduced by half in time `t_(2)`
`C"" = ( C)/(2)`
`V_(0)//(2)= V_(0)//(e)^(-((t_(2))/(RC//2)))`
Divide equation (i) by (ii)
`(t_(2))/((RC)/(2))=(10)/(2RC)`
`t_(2)= 2.5` seconds .