1. The problem statement, all variables and given/known data A circuit is powered by a 10 V power supply and has a resistor of 500 ohms in series with a capacitor. After 4 seconds, the value of ln(1-(Vc/Vo)) is -2, where Vc is the voltage in the capacitor at a given time and Vo is 10 V. 1) Find the capacitance. 2) Find how long it takes for the potential difference across the capacitor to rise from 0 V to 4 V. 2. Relevant equations Vc = Vo(1 - e^(-t/RC)) Tau = RC 3. The attempt at a solution ln(1-(Vc/Vo))/t = -2/4 = 0.5 Let's try to figure out what this represents Vc = Vo(1 - e^(-t/RC)) ln Vc = ln Vo(1 - e^(-t/RC)) ln Vc = ln Vo + ln(1 - e^(-t/RC)) ln Vc - ln Vo = ln(1 - e^(-t/RC)) Vc/Vo = 1 - e^(-t/RC) e^(-t/RC) = 1 - Vc/Vo -t/RC = ln(1 - Vc/Vo) -1/RC = ln(1 - Vc/Vo)/t = -0.5 So I have 1/RC = 0.5, therefore the time constant Tau = RC = 2 seconds. 1) (500)(C) = 2 -> Capacitance = 0.004 F 2) If -t/RC = ln(1 - Vc/Vo) then t = -RC*ln(1 - Vc/v0) = -2*ln(1-4/10) = 1.021 seconds. Is this correct? I've been told that I have a mistake somewhere, but I don't know where.