A capacitor having initial charge q₀ and capacitance C is connected to a variable resistance R. The resistance R can have values ranging from 0 to R₀. How should we vary R with time (t) such that the discharging current remains constant with time?
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Question

A capacitor having initial charge q₀ and capacitance C is connected to a variable resistance R. The resistance R can have values ranging from 0 to R₀. How should we vary R with time (t) such that the discharging current remains constant with time?

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G1 Physics · Accepted Answer

For constant discharge current I, q = q₀ - It and capacitor voltage V = q/C. Since I = V/R, R = q/(CI) = q₀/(CI) - t/C. Taking initial resistance R₀ = q₀/(CI), R(t)=R₀-t/C.