Physics!! Help!!!!!
posted by Mary on .
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.

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 
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