Consider the circuit shown for which R 1 =2.2 M?, R 2 =1.3 M?, R 3 =3.5 M?, C=7.
ID: 1396905 • Letter: C
Question
Consider the circuit shown for which R1=2.2 M?, R2=1.3 M?, R3=3.5 M?, C=7.3 ?F,and V=39.0 V. For charging, we open S2 and close S1. For discharge, after a full charge, we open S1 then close S2.
a) What is the charge time constant for the circuit? Answer in units of seconds.
b) What is the discharge time constant for the circuit? Answer in units of seconds.
After fully discharging the circuit, we close S2 and then close S1. The capacitor will charge.
c) What is in micro-amps the current through R2 once the capacitor is fully charged?
d) What is in micro-amps the current through R1 once the capacitor is fully charged?
e) What is in volts, the voltage across the capacitor once it is fully charged?
Explanation / Answer
a)
S1 is closed , S2 is Open
Total resistance of circuit = R = R1 + R2 = 2.2 + 1.3 = 3.5 x 106 ohm
C = 7.3 x 10-6 F
Time constant is given as :
T = RC = (3.5 x 106 ) (7.3 x 10-6 ) = 25.55 sec
b)
S2 is closed , S1 is Open
Total resistance of circuit = R = R2 + R3 = 1.3 + 3.5 = 4.8 x 106 ohm
C = 7.3 x 10-6 F
Time constant is given as :
T = RC = (4.8 x 106 ) (7.3 x 10-6 ) = 35.04 sec
c)
once the capacitor is fully charged, the branch containing the capacitor becomes open circuit and no current flow through that branch . hence current through R2 = 0
d)
Total resistance.R = R1 + R3 = 2.2 + 3.5 = 5.7 x 106 ohm
V = Voltage = 39 volts
current is given as :
i = V/R = 39 / (5.7 x 106) = 6.84 uA
e)
Voltage across R3 = Voltage across C = i R3 = (6.84 x 10-6) (3.5 x 106) = 23.94 volts