The plates of a capacitor are charged to a potential difference of $320 \, volts$ and are then connected across a resistor. The potential difference across the capacitor decays exponentially with time. After $1 $ second the potential difference between the plates of the capacitor is $240 \, volts$, then after $2$ and $3$ seconds the potential difference between the plates will be
Diffcult
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(b) $V = {V_0}({e^{ - \lambda t}})$
After $1$ seconds
${V_1} = 320({e^{ - \lambda }}) \Rightarrow 240 = 320({e^{ - \lambda }})\, \Rightarrow \,{e^{ - \lambda }} = \frac{3}{4}$
After $2$ seconds
${V_2} = 320\,{({e^{ - \lambda }})^2} = 320 \times {\left( {\frac{3}{4}} \right)^2} = 180\,\,volt$
After $3$ seconds
${V_3} = 320\,{({e^{ - \lambda }})^3} = 320 \times {\left( {\frac{3}{4}} \right)^3} = 135\,\,volt$
After $1$ seconds
${V_1} = 320({e^{ - \lambda }}) \Rightarrow 240 = 320({e^{ - \lambda }})\, \Rightarrow \,{e^{ - \lambda }} = \frac{3}{4}$
After $2$ seconds
${V_2} = 320\,{({e^{ - \lambda }})^2} = 320 \times {\left( {\frac{3}{4}} \right)^2} = 180\,\,volt$
After $3$ seconds
${V_3} = 320\,{({e^{ - \lambda }})^3} = 320 \times {\left( {\frac{3}{4}} \right)^3} = 135\,\,volt$
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