Answer:
t = 0.731s
Explanation:
In order to calculate the time that the capacitor takes to have a voltage of 70V, you use the following formula:
[tex]V=V_oe^{-\frac{t}{RC}}[/tex] (1)
V: final voltage across the capacitor = 70V
Vo: initial voltage across the capacitor = 100V
R: resistance of the resistor in the circuit = 1kΩ = 1*10^3Ω
C: capacitance of the capacitor = 2mF = 2*10^-3F
t: time
You use properties of logarithms to solve the equation (1) for t:
[tex]\frac{V}{V_o}=e^{-\frac{t}{RC}}\\\\ln(\frac{V}{V_o})=ln(e^{-\frac{t}{RC}})\\\\ln(\frac{V}{V_o})=-\frac{t}{RC}\\\\t=-RCln(\frac{V}{V_o})[/tex]
Next, you replace the values of the parameters:
[tex]t=-(1*10^3\Omega)(2*10^{-3})ln(\frac{70V}{100V})\\\\t=0.713s[/tex]
The capacitor takes 0.731s to reache a voltage of 70V
