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)

$Q=c\varepsilon_{0}\,e^{-tcR}$
$4\varepsilon=4\varepsilon_{0}\,\varepsilon^{-t\tau}$
$\varepsilon=\varepsilon_{0}\,\varepsilon^{-t\tau}$
When $t = 0 \Rightarrow \varepsilon_{0}=25$
$\varepsilon=\varepsilon_{0}=25$
When $t = 200 \Rightarrow \varepsilon =5$
$5=25\,e^{-\frac{200}{\tau}}$
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 × 25 = 9.25 V$
Which time in $100 < t < 150$ sec.