How Do Resistors and Nodes Function in a Parallel Circuit?

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SUMMARY

This discussion focuses on the function of resistors and nodes in a parallel circuit, specifically analyzing a circuit with two 3 Ohm resistors, a 6 Ohm resistor, and a 12 Ohm resistor. It clarifies that for resistors to be in parallel, they must be connected between the same two nodes, which are points in the circuit where the electric potential is uniform. The participants suggest combining resistors in series to simplify the circuit analysis, resulting in three resistors in parallel for further calculations.

PREREQUISITES
  • Understanding of Ohm's Law (I=V/R)
  • Familiarity with series and parallel resistor configurations
  • Knowledge of circuit nodes and their significance
  • Basic proficiency in electrical power calculations (P=VI, P=(I^2)(R), P=(V^2)/R)
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  • Study the role of nodes in circuit analysis
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Homework Statement


http://img487.imageshack.us/img487/2263/physicsqh1.png
Shot at 2007-07-23


Homework Equations


I=V/R
V=IR
R=V/I
P=VI
P=(I^2)(R)
P=(V^2)/R


The Attempt at a Solution



Just a Quick Question, are both of the 3 Ohms parallel?? as well as the 6hom and the 12 Ohm?

Also what exactly do nodes do (there should be little dots on the corners of the top and bottom diagonals "\/" and the "^"
 
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The two 3ohm resistors aren't connected in parallel, in order to have two resistors in parallel their terminal must be the same, that is they must be connected between the same two nodes. A node is a portion of the circuit were the electric potential is the same everywhere, that is a wire were there isn't a potential difference. To analyze this circuit you could associate the left 3ohm resistor with the 6ohm resistor and replace it by an equivalent 3+6=9ohm resistor, because they are in series, and you could associate the 12ohm and the right 3ohm resistor too, the same way. Then you would get three resistors in parallel.
 

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