A circuit is constructed with four resistors, one capacitor, one battery and a s

Question

A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1-R2-59 , R3 48 and R4-93 . The capacitance is C = 49 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 11 (0), the magnitude of the A 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? A Submit 3) What is Q), the charge on the capacitor after the switch has been closed for a very long time? C Submit

Explanation / Answer

1) When the switch is first thrown the capacitor won’t have any charge on it and thus no voltage drop.The current will want to flow down this easier rout and will completely ignore the R3 path.Thus taking a Kirchoff loop

we have V- R1*I1- R4*I1 = 0 which gives I1=0.158 A

2) A long time after the switch has been closed the charge on the capacitor will be full and the current through the capacitor path will become zero.The current will then flow down the alternate R2R3path and taking aKirchoff loop we get V- I1*R1- I1*R2- I1*R3- I1*R4 =0 which gives I1=0.093 A

3) For this one we need to take two Kirchoff loops:The first on the path that ignores the capacitor and the second on the loop that incorporates the capacitor and R2 and R3 so,V- I1*R1- I1*R2- I1*R3- I1*R4 =0

and –Q/C +I1*R3 +I1*R2 =0

Q = C[I1*R3 +I1*R2] = 487.6 nC

4) Once again just after the circuit is closed we get no voltage loss across the capacitor but since there’s resistors in both pathways we’ll get current through both.First we add R2 and R3 in series.Then we add R5 and R2,3 in parallel remembering that they add inversely.Then we add R1 R2,3,5 and R4 n series and takeV/Rnet=I

I = 24/198.74 = 0.121 A

5) We get the exact same result as in 3 because there’s no current through the capacitor path at large times and so when we add up our Kirchhoff loops, R5 has no effect.

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