Question

The figure shows an experimental plot discharging of a capacitor in an $RC$ circuit. The time constant $\tau$ of this circuit lies between :

• A. 150 sec and 200 sec
• B. 0 and 50 sec
• C. 50 sec and 100 sec
• D. 100 sec and 150 sec

Answer 1

Answer: (D)

$Q=c{\epsilon }_0{e}^{-tcR}$
$4\epsilon =4{\epsilon }_0{\epsilon }^{-t\tau }$
$\epsilon ={\epsilon }_0{\epsilon }^{-t\tau }$
When $t=0\Rightarrow {\epsilon }_0=25$
$\epsilon ={\epsilon }_0=25$
When $t=200\Rightarrow \epsilon =5$
$5=25e^{-\frac{200}{\tau }}$
In $5=e^{-\frac{200}{\tau }}$
$\tau =\frac{200}{\ell n5}=\frac{200}{\ell n10-\ell n2}$
$=\frac{200}{\ell n10-0.693}$
Alternative :
Time constant is the time in which 63% discharging is completed.
So remaining charge$=0.37\times 25=9.25V$
Which time in $100<t<150$ sec.