Kirchhoff's rules for resistors in parallel

In summary, the conversation discusses using Kirchoff's rules to determine the currents I1, I2, and I3 for a circuit with an EMF of 9V and resistors with values of 1.5, 5, 15, and 13.75. The attempt at a solution involves using equations such as 0=ε-I1r-IR1-IR2 and 0=ε-I1r-I3R3 to find the values of I1, I2, and I3. The circuit is also suggested to be redrawn in a more conventional way using standard schematic symbols for easier analysis.
  • #1
coleman221
2
0

Homework Statement



25tko42.jpg


Use Kirchoff's rules to determine I1, I2 and I3 for the following circuit:
Use the following values:ε = emf = 9 V
r = internal resistance = 1.5
R1 = 5
R2 = 15
R3 = 13.75

Homework Equations



The Attempt at a Solution


I found I1 to be .9328 by adding all the resistors together (taking into account that r3 was in parallel to r1 and r2) and adding the resistance of the battery.

I've been trying to use 0=ε-I1r-IR1-IR2
0=ε-I1r-I3R3
I1=I2+I3
I've done similar problems but this is for a lab instead of homework so its written in different a way (and they like to throw in things we haven't learned yet in lecture) so i think I'm having trouble visualizing where the currents are splitting and what parts are equivalent.
 
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  • #2
updated to add correct image
 
  • #3
Why not redraw the circuit in a more conventional way, using the standard schematic symbols? It might help you to see ways to go about analyzing it.
 

1. What are Kirchhoff's rules for resistors in parallel?

Kirchhoff's rules for resistors in parallel state that the total current entering a junction in a parallel circuit is equal to the sum of the currents through each individual branch. Additionally, the total resistance in a parallel circuit is equal to the reciprocal of the sum of the reciprocals of each individual resistance.

2. Why are Kirchhoff's rules important in circuit analysis?

Kirchhoff's rules are important in circuit analysis because they provide a systematic way to analyze complex circuits and determine the values of currents, voltages, and resistances. They are based on the fundamental principles of conservation of energy and conservation of charge.

3. Can Kirchhoff's rules be applied to other types of circuits?

Yes, Kirchhoff's rules can be applied to any type of circuit, including series circuits, parallel circuits, and more complex circuits with multiple loops and branches. They are fundamental principles in circuit analysis and can be used to solve a wide range of electrical engineering problems.

4. How do Kirchhoff's rules account for the behavior of resistors in parallel?

Kirchhoff's rules account for the behavior of resistors in parallel by considering the individual currents and resistances in each branch of the circuit. The rules state that the total current entering a junction must be equal to the sum of the currents through each branch, and the total resistance in the circuit must be equal to the reciprocal of the sum of the reciprocals of each individual resistance.

5. Are there any limitations to Kirchhoff's rules for resistors in parallel?

Kirchhoff's rules for resistors in parallel are accurate and useful for analyzing most circuits, but they do have some limitations. They assume that the resistors are connected in parallel, and any deviations from this configuration may cause the rules to not apply. Additionally, the rules may not be applicable in circuits with non-linear components, such as diodes or transistors.

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