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 = 58 , R3 = 48 and R4 = 93 . The capacitance is C = 48 F and the battery voltage is V = 24 V.

I only need #4,5. They are supposed to be tricky, so If you are not sure about the answer, please don't answer at all. Thank you.

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?

= .1589 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?

=.09338 A

3)

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

= 475.14 C

4)

Consider the circuit above, with R5 = 83 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

4) Consider the circuit above, with R5 = 83 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?
Uncharged capacitors are modeled as short circuits at t=0
The resistance seen by the source = (48+58)||83 + (58+93) = 197.55
I1(0) = 24/197.55 = 0.1214A <------------

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
A charged capacitor is modeled as an open circuit
Vc = 24/(58+58+48+93) * (58+48) = 9.8988 V
Q = C*V = 48e-6*9.8988 = 0.475mC = 475.14C <------------

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