[Circuits] Calculating voltage and current in a circuit

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Discussion Overview

The discussion revolves around calculating voltage and current in a circuit, specifically focusing on the application of Kirchhoff's Current Law (KCL) and the equivalent resistance of resistors in parallel. It includes elements of homework-related problem-solving and technical explanation.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the equation used by the author, specifically $$v_{ i }=2li=42V$$, seeking clarification on the underlying equation.
  • Another participant asserts that the correct equivalent resistance for the parallel combination of the 70 Ω and 30 Ω resistors is 21 Ω, suggesting that the voltage drop is calculated across this pair.
  • A participant notes that KCL was applied at a middle node with the equation $$i_1=i_2+I_0$$, but raises a concern about whether the analysis adequately considers the other side of the node.
  • In response, another participant defends the approach, suggesting that the current $$I_0$$ accounts for the conditions on the other side of the node and proposes a conceptual model of the horizontal wire as a zero ohm resistor separating two nodes.

Areas of Agreement / Disagreement

Participants express differing views on the application of KCL and the treatment of the node in question. There is no consensus on whether the analysis is complete or acceptable.

Contextual Notes

The discussion highlights potential limitations in the analysis, particularly regarding the assumptions made about the node and the treatment of currents on both sides. The resolution of these points remains unclear.

ainster31
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Homework Statement



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Homework Equations





The Attempt at a Solution



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How does the author do the below?

$$v_{ i }=2li=42V$$

What equation is he/she using?
 
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That should be 21i. 21 Ω is the parallel combination of the 70 Ω and 30 Ω resistors. The author is calculating the voltage drop across that pair.
 
gneill said:
That should be 21i. 21 Ω is the parallel combination of the 70 Ω and 30 Ω resistors. The author is calculating the voltage drop across that pair.

They seemed to have applied KCL at the middle node: $$i_1=i_2+I_0$$

But what about the other side of the same node? It looks like they only looked at the left-side of that node. Is that acceptable?
 
ainster31 said:
They seemed to have applied KCL at the middle node: $$i_1=i_2+I_0$$

But what about the other side of the same node? It looks like they only looked at the left-side of that node. Is that acceptable?

The current Io takes care of whatever is happening on the other side; the node was partitioned in order to "get at" the current Io . If you want, think of the horizontal wire as a zero ohm resistor separating two nodes :smile:
 

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