When connected to earth, any charged capacitor will discharge, and the voltage across the capacitor will decrease. This is modelled by the differential equation dV/dT=-V/RC, where V = voltage, and R and C (resistance in ohms and capacitance in farads respectively) are constants. If V drops from 10 volts to 1 volt in two seconds, and is C = 3*10^-6 farads, determine the value of R.

dV/dt = -V / RC

dV/V = -dt / RC

V(t) = V(0)e

^{-t / RC}C = 3 x 10

^{-6}FV(0) = 10

V(2) = 1

V(2) / V(0) = e

^{-2 / RC}1/10 = e

^{-2 / RC}= 0.1-2 / RC = ln(0.1)

R = -2 / [C ln(0.1)] = -2 / [(3 x 10

^{-6}F) ln(0.1)] ≅ 289,530 Ω
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