Question

The plates of a capacitor are charged to potential difference of V volts and then connected across a resistor. The potential difference across the capacitor decreases exponentially with respect to time. After one second, the potential difference between the plates is V/3; then after two seconds from the start the potential difference between the plates is :

• A. V/27
• B. V/6
• C. V/9
• D. V/3

Answer 1

The correct option is A V/27

$V=V_0{e}^{-\alpha t}$

$\frac{V}{3}=V{e}^{-\alpha }$

$e^{-\alpha }=\frac{1}{3}$

$V_2=V_0{\left(e^{-\alpha }\right)}^2$

$V{\left(\frac{1}{3}\right)}^2=\frac{V}{9}$

$V_3=V{\left(e^{-\alpha }\right)}^3$

$=\frac{V}{27}$