JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Modern Physics

A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance

200 μ F

is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be

____

Ω

Answer: 150

Solution

The activity falls as

A = A_{0} e^{- t / τ}

with

τ = 30

ms the average life, while the charge on the capacitor discharging through

R

falls as

q = q_{0} e^{- t / R C}

. A ratio

q / A

that does not drift with time demands equal exponents, so

R C = τ

and

R = \frac{τ}{C} = \frac{30 \times 1 0 ^{- 3}}{200 \times 1 0 ^{- 6}} = 150

The resistance must be

150 Ω

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Integer answer

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