A radioactive sample decays with an average life of `20 ms`. A capacitor of capacitance `100 muF` is charged to some potential and then the plates are connected through a resistance `R`. What should be the value of `R` so that the ratio of the charge on the capacitor to the activity of the radioactive sample remains constant in time?
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Here, `tau=20milli sec=20xx10^(-3)s, C=100mu F=100xx10^(-6)F`. The activity of the sample at time t is ` A=A_(0)e^(-lambdat)` Charge on the capacitor at time t is `Q=Q_(0)e^(-t//RC)` `Q/A=(Q_(0)e^(-t//RC))/(A_(0)e^(-lambdat))` Clearly, the ratio will be independent of t, if `lambda=1/(RC) or R=1/(lambdaC)=tau/C=(20xx10^(-3))/(100xx10^(-6))=200ohm`
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