A radioactive sample has mean life 20 ms. A 100 μF capacitor discharges through resistance R. Find R so that the ratio of capacitor charge Q(t) to radioactive activity A(t) remains constant in time. Give R in Ω.
Physics · Nuclear physics
JEE Advanced Practice

Question

A radioactive sample has mean life 20 ms. A 100 μF capacitor discharges through resistance R. Find R so that the ratio of capacitor charge Q(t) to radioactive activity A(t) remains constant in time. Give R in Ω.

Physics · Nuclear physics

G1 Physics · Accepted Answer

Radioactive activity decays as e⁻ᵗᐟτ with τ=20 ms. Capacitor charge decays as e⁻ᵗᐟᴿᶜ. For Q/A constant, RC=τ. Hence R=τ/C=20×10⁻³/(100×10⁻⁶)=200 Ω.