Question

A resistor and a capacitor are connected as shown in the figure. The capacitor is originally given a charge of $5.0\mu \text{C}$ and then discharged by closing the switch at $t=0$. At what time will the charge be equal to $0.50\mu \text{C}$. Given, $C=1\mu \text{F},R=10\text{M}\Omega ,$ $\ln \left(0.1\right)=-2.3$

• A. $23\text{s}$
• B. $22\text{s}$
  
• C. $21\text{s}$
  
• D. $20\text{s}$
  

Answer 1

The correct option is A $23\text{s}$

Given,

Initial charge, $Q=5\mu \text{C}$,

Final charge, $q=0.5\mu \text{C}$,

$C=1\mu \text{F},R=10\text{M}\Omega$,

For time $t$, we have $$t=-RC\ln \frac{q}{Q}$$ $\Rightarrow t=-10\times {10}^6\times 1.0\times {10}^{-6}\ln \frac{0.50}{5.0}$

$\Rightarrow t=23\text{s}$

Hence, option (a) is the correct answer.