An RC circuit lakes t 199 s to charge to 65 when a voltage

An RC circuit lakes t = 1.99 s to charge to 65% when a voltage of AV = 45 V is applied. Randomized Variables t = 1.99 s Del V = 4.5V p = 65%. What is this circuit\'s time constant r, in seconds?

Solution

A)

we know that voltage across capacitor after t sec is

v = Vmax*(1-e^(-t/T))

0.65*Vmax = Vmax*(1-e^(-1.99/T))

1-e^(-1.99/T) = 0.65

e^(-1.99/T) = 0.35

-1.99/T = ln(0.35) = -1.04

T = 1.99/1.04

T = 1.91 sec is the required time constant

b) T = R*C

C =T/R = 1.91/6.5 = 0.293 F

C) Qmax = C*V = 0.293*4.5 = 1.32 C