The figure below shows how a bleeder resistor (R = 246 k omega) is used to disch

Question

The figure below shows how a bleeder resistor (R = 246 k omega) is used to discharge a capacitor (c = 71.7 muF) after an electronic device is shut off, allowing a person to work on the electronics with less risk of shock. What is the time constant? s How long will it take to reduce the voltage on the capacitor to 0.100 Percentage of its full value once discharge begins? s If the capacitor is charged to a voltage V_0 through a 153 omega resistance, calculate the time it takes to rise to_0.865V_0 (This is about two time constants). s

Explanation / Answer

a) the time constant is

= R C = ( 246x103 ) ( 71.7x10-6 F ) = 17.6 s

b) from the voltage of the capacitor is

V(t) = V0 e-t/   

then the time is

t = - ln ( V(t) / V0 )

if V(t)= 0.100% V0 = 0.001 V0 hence

t = - ln ( (0.001 V0)/ V0 )

t = -( 17.6 s ) ln ( 0.001 )

t = 121.6 s

c) in charge

V(t) = V0 [ 1 - e-t/RC ]

then

t = -R C ln ( 1- V(t) / V0 )

if V(t) = 0.865 V0

t = -R C ln ( 1- ( 0.865 V0  ) / V0 )

t = -R C ln ( 1- 0.865 )

t = -( 153 ) ( 71.7x10-6 F ) ln ( 1- 0.865 )

t = -( 153   ) ( 71.7x10-6 F ) ln ( 1- 0.865 )

t = 0.022 s

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