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 = 62 , R3 = 51 and R4 = 134 . The capacitance is C = 78 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 I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?A

2)What is I1(), the magnitude of the current that flows through the resistor R1 a very long time after the switch has been closed?A

3)What is Q(), the charge on the capacitor after the switch has been closed for a very long time?C

4)

Consider the circuit above, with R5 = 124 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 I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?A

5)Continuing with the new circuit, what is Q(), the charge on the capacitor after the switch has been closed for a very long time?C

Explanation / Answer

According to the question provided we know that

Req =R1+R4 =62 + 134

Req =196 ohms

I1(0)=V/Req =24/196

I1(0) =0.1224489A ===A)

part b)

Req=R1+R2+R3+R4 =78+78+67+62

Req=309 ohsm

I1(inf) =V/Req =24/309

I1(inf) =0.0776699 A ======B)

part c)

V(inf) =I(inf)*(R2+R3) =0.0776699*(113) =8.776698 V

Q(inf)=C*V(inf) =78*8.776698

Q(inf) =684.5824 uC

part d)

Req =R1+R4+(R5||(R2+R3)

Req=62+134+(113*124/113+124)

Req=255.122 ohsm

I1(0) =V/Req =24/255.122

I1(0) =0.094072 A ======D)

Allowed to answer only 4 sub parts at a time According to the chegg guidelines.

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