# Physics!! Help!!!!!

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The time dependence of voltage across a discharging capacitor is given by the exponential decay. The voltage on the capacitor at time t= 0 sec is 24 volt. If a 220 +/- 22uF capacitor and 1 Mega ohm (5% tolerance) resistor are used in the RC circuit, what would be the value of the time constant (T=RC) and the associated error? What would be the voltage V after t = 100 sec? Propagate the errors and find the percent error in the voltage V.

• Physics!! Help!!!!! - ,

C = q/V
q = C V
i = -dq/dt = -C dV/dt
but V = i r
so
i = -C r di/dt

i + C r di/dt = 0
V/r + C r (1/r) dV/dt) = 0
V + r C dV/dt = 0

dV/dt = -1/rC V
dV/V = -1/rC dt
ln V = - (1/rC) t
V = Vi e^-(1/RC)t

• Physics!! Help!!!!! - ,

let T = RC
then
V = Vi e^-t/T

if RC = 10^6 * 220*10^-6 = 220 = T
Vi = 24
V = 24 e^-t/220

if t = 100
V = 24 e^-(100/220) = 24 e^-.454
= 24*.635 = 15.2

You can do the change for new C and R and get error in V

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