A charged capacitor of capacitance C is discharged through a resistance R. A radioactive sample decays with an average-life `tau`.Find the value of R for which the ratio of the electrostatic field energy stored in the capacitor to the activity of the radioactive sample remains constant in time.

Options

A. `(2t)/(C )`
B. `(C )/(2t)`
C. `2tC `
D. `tC`

Answer

A

Explanation

`(U_(c))/(A)` = constant,` ((1)/(2) CV_(0)^(2))/(lamda N _(0)) = ((1)/(2) CV ^(2))/(lamda N)`
where `V = V_(0)e ^(-t//CR),` N = N _(0) e ^(- lamda t) and lamda = (1)/(t)`