Finding the magnitude and direction of current thro Kirchhoff law

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SUMMARY

The discussion centers on calculating the magnitude and direction of current through a 10 ohm resistor using Kirchhoff's laws. The book states the current is 1/23 Ampere from A to B, while the user calculated it as 5/37 Ampere (approximately 0.13514A) using the superposition principle. The user verified their calculations by shorting voltage sources and summing voltages, concluding that the book's answer is incorrect. The correct current direction is from A to B, confirming the user's approach and results.

PREREQUISITES
  • Understanding of Kirchhoff's laws
  • Familiarity with the superposition principle in circuit analysis
  • Basic knowledge of Ohm's law
  • Ability to analyze circuits with multiple voltage sources
NEXT STEPS
  • Study Kirchhoff's Voltage Law (KVL) in detail
  • Learn advanced techniques for circuit analysis, such as Thevenin's and Norton's theorems
  • Practice problems involving superposition in electrical circuits
  • Explore simulation tools like LTspice for circuit analysis
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Electrical engineering students, circuit designers, and anyone involved in analyzing electrical circuits using Kirchhoff's laws.

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Homework Statement



Revered Members,
Please go through my attachment. I have been asked to find the magnitude and direction of current through the 10 ohm resistor. The answer that is given in the book is 1/23 Ampere from A to B.
But i solved as given in the attachment but i got the answer as 5/37 Ampere which is I3...the current which I assumed to pass through 10 ohm resistor. Since Please help me where i went wrong.

Homework Equations





The Attempt at a Solution


 

Attachments

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Your work and results look fine. Must be an error in the book's answer.
 
I used the superposition principle as follows:

1. Short the 2V source & get voltage across the 10Ω = +2.1622V.
2. Short the 8V source and get same voltage = -0.8108V
3. Superpose the voltages to get +1.3514V across the 10Ω.
4. Divide by 10Ω to get i3 = 0.13514A which agrees with both of you!
 
Thank you gneill and rude man for your help.
 

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