Q. Combination of two identical capacitors, a resistor $R$ and a DC voltage source of voltage 6 V is used in an experiment on$C - R$ 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 10s. For series combination the time needed for reducing the voltage of the fully charged series combination by half is
A) 200s
B) 10s
C) 5s
D) 2.5s
Explanation
(d) If $C_{e}$ be the effective capacitance, then
$V_{C} = \frac{1}{2}V_{0}$
$\frac{q}{C_{e}} = \frac{q_{0}}{2C_{e}}$
$\Longrightarrow q_{0}\left( 1 - e^{- \frac{t}{RC_{e}}} \right)\ = \frac{q_{0}}{2}$
$\Longrightarrow \ \ \ \ t = RC_{e}\ \ In2$
For parallel grouping
$C_{e} = \frac{2C}{2}$
$\therefore\ \ t_{2} = 2RC\ In2$
For series grouping
$C_{e} = \frac{C}{2}$
$t_{1} = \frac{RC}{2}In\ 2$
$\frac{t_{2}}{t_{1}} = \frac{1}{4}t_{2} = 2.5s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.