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Q.

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

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a

180 and 135 V

b

160 and 80 V

c

200 and 180 V

d

140 and 20 V

answer is B.

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Detailed Solution

$V = {V_0}({e^{ - \lambda t}})$ 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

${V_3} = 320\,{({e^{ - \lambda }})^3} = 320 \times {\left( {\frac{3}{4}} \right)^3} = 135\,\,volt$

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