Finding the magnitude and direction of current thro Kirchhoff law

AI Thread Summary
The discussion focuses on calculating the current through a 10-ohm resistor using Kirchhoff's laws. The original poster's calculation yielded a current of 5/37 Ampere, while the book states it should be 1/23 Ampere. Other members confirmed the poster's calculations, indicating the book's answer is likely incorrect. By applying the superposition principle, they found the voltage across the resistor to be 1.3514V, resulting in a current of 0.13514A. The consensus is that the book's answer does not align with the correct calculations.
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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

  • prob.jpg
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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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