A charged capacitor of capacitance C is discharged through a resistance R. A radioactive sample decays with an average-life τ. 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.

Question

Philoid · Accepted Answer

Let charge at time t be Q and initial charge be q. Q is given by Q= q

And according to Law of Radioactivity,

A= A˳e^-λt

So, =

(where C is the capacitance, R is the resistance, t is the time, q is the charge, λ is the decay constant)

As the ratio should be independent of time,

∴

_R=