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

The Correct Option is 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.