Two Loop RC Circuit 1 1 2 34 5 6 A circuit is constructed with four resistors, o
ID: 1592301 • Letter: T
Question
Two Loop RC Circuit 1 1 2 34 5 6 A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 43 , R3 = 72 and R4 = 105 . The capacitance is C = 87 F and the battery voltage is V - 24 V. 1) The switch has been open for a long time when at time t 0, the switch is closed. What is l1(0), the magnitude of the current through the resistor R1 just after the switch is closed? Submit 2) What is 11(), the magnitude of the current that flows through the resistor R1 a very long time after the switch has been closed? Submit 3) What is Q(), the charge on the capacitor after the switch has been closed for a very long time? HC Submit 4) Consider the circuit above, with R5 = 95 in series with the capacitor. Once again, the switch has been open for a long time when at time t - 0, the switch is closed. What is l1(0), the magnitude of the current through the resistor R1 just after the switch is closed? Submit 5) Continuing with the new circuit, what is Q(o°), the charge on the capacitor after the switch has been closed for a very long time? SubmitExplanation / Answer
1) At t = 0, the capacitor will behave like a short circuit hence only R1 and R4 will be in circuit others won't be a part of circuit.
Hence I1 = V/(R1+R4) = 24/(43+105) = 162 mA
2) After a long time the capacitor will be fully charged hence will behave like a open circuit then resistors R1,R2,R3 and R4 will be in series.
The current I1 = V/(R1+R2+R3+R4) = 24/(43+43+72+105) = 91.25 mA
3) The voltage across capacitor will be,
Vc = I*(R2+R3) = 91.25*(43+72) = 10.49 V
The charge on capacitor Q = CVc = 87*10.49 uC = 913 uC
4) The equivalent resistance of the circuit:
R = R1 +R5||(R2+R3)+R4 = 52+43+105 = 200 ohm
current I1 = 24/200 = 120 mA
5) This will also be the same:
Q = 913 uC.
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