Question

Figure 20.47 shows how a bleeder resistor (R = 260 kohm) is used to discharge a capacitor (c = 70.mu F) after an electronic device is shut off, allowing a person to work on the electronics with less risk of shock. (a) What is the time constant? s (b) How long will it take to reduce the voltage on the capacitor to o.300% of its full value once discharge begins? s (c) If the capacitor is charged to a voltage V_0 through a 125 ohm resistance, calculate the time it takes to rise to 0.865V_0 (this is about two time constants) s

Answer 1

a) Time constant of a prallel RC circuit, T = RC
R = 260,000 ohm
C = 70 mu F
T = 260,000 * 70/1000,000 = 18.2 s
b) initial voltage = Vo
voltage discharge equation of capacitor, V = Vo*exp(-t/T)
now, V = 0.3Vo/100
so, 0.003 = exp(-t/18.2)
t = 105.726 s
c) initial voltage = 0
maximum voltage = Vo
charging equation
V = Vo(1 - exp(-t/T))
0.865 = 1 - exp(-t/18.2)
t = 36.4451 s