RC Circuit Problem: Find I1, I2, I3 and Q

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SUMMARY

The discussion focuses on solving an RC circuit problem involving three resistors (R1 = 12.0 kΩ, R2 = 17.0 kΩ, R3 = 1.00 kΩ) and a voltage source (V = 9.70 V). Participants aim to calculate the steady-state currents (I1, I2, I3) and the charge on the capacitor. The key takeaway is that the voltage divider effect must be considered to accurately determine the current through each resistor, as the voltage across the capacitor stabilizes in steady state.

PREREQUISITES
  • Understanding of Ohm's Law (R = V / I)
  • Knowledge of RC circuit behavior in steady state
  • Familiarity with voltage dividers
  • Basic capacitor charge equations (q = Q e^(-t/RC))
NEXT STEPS
  • Calculate steady-state currents in RC circuits using voltage dividers
  • Explore the impact of resistor values on current distribution
  • Study capacitor charging equations in detail
  • Learn about transient analysis in RC circuits
USEFUL FOR

Students studying electrical engineering, circuit analysis enthusiasts, and anyone looking to deepen their understanding of RC circuits and steady-state behavior.

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Homework Statement



In Figure P18.50, suppose that the switch has been closed for a length of time sufficiently long enough for the capacitor to become fully charged. (R = 12.0 k, R2 = 17.0 k, R3 = 1.00 k, V = 9.70 V)

The picture is under attachment

a) Find the steady-state current in each resistor.
I1 = µA?
I2 = µA?
I3 = µA ?

(b) Find the charge on the capacitor.
µC ?


Homework Equations



R = V / I

q = Q e^(-t/RC)

The Attempt at a Solution



Well, since after the switch is closed, I figured all 9.7 V goes to the first resistor, so I used R = V / I to get the current for the first one. But it's wrong.
 

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It's wrong because there is a voltage divider formed with one of the other two resistors in the steady state. Which one? In the steady state, what is the voltage across the capacitor?
 

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