Posted by **Mary** on Thursday, January 26, 2012 at 10:45pm.

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!!!!! -
**Damon**, Thursday, January 26, 2012 at 11:03pm
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!!!!! -
**Damon**, Thursday, January 26, 2012 at 11:12pm
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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