# Kirchoff law problem

Discussion in 'Homework Help' started by logearav, Dec 28, 2012.

1. ### logearav Thread Starter Member

Aug 19, 2011
248
0
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.

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2. ### mrmount Active Member

Dec 5, 2007
59
7
I got the same answer too!

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3. ### MKCheruvu Member

Nov 20, 2012
30
6
Solving this problem by super position theorem :
Ir10 due to 8v source = 16/74 and
Ir10 due to -2Vsource = -6/74
Net Ir10 Current = 10/74 =5/37

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4. ### WBahn Moderator

Mar 31, 2012
23,552
7,207
Yet another approach:

Remove the 10Ω resistor and find the Thevenin equivalent between A and B for the rest of the circuit.

Rth = 12Ω||8Ω = 96Ω^2 / 20Ω = 4.8Ω

Vth = -2V + 10V(8Ω/20Ω) = +2V

Now put the 10Ω resistor back in and you have:

I = 2V/(10Ω + 4.8Ω) = (1/7.4)A = (5/37)A

The Point: If you can work the problem several different ways and all produce the same answer, then there is good reason to believe that your answer is correct and the book is wrong (unless every method you used had some flaw in common -- so be sure to be on the lookout for that).

Yet another approach:

You come up with an answer of (5/37)A. So check the validity of the answer starting from the answer itself:

V_B = 0V (I'm defining B to be ground). This means that

V_A = (50/37)V

This makes the current toward A from the left

I_12 = [8V - (50/37)V]/12Ω = [246/(37*12)]A =(41/74) A

Likewise, the current toward A from the right:

I_8 = [-2V - (50/37)V]/8Ω = [-124/(37*8)]A =(-31/74) A

Now we can see if KCL is truly satisfied at Node B:

I_12 + I_8 =? (5/37)A

(41/74)A - (31/74)A = (10/74)A = (5/37)A

The Point: In a surprisingly large number of problems, both in school and in the real world, it is possible to verify the correctness of your answer from the answer itself. Get in the habit of doing so. You grades will probably take a significant turn for the better and you will be less likely to kill someone down the road because of an undetected error.

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5. ### sleet1986 New Member

Dec 29, 2012
2
1

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6. ### JoeJester AAC Fanatic!

Apr 26, 2005
3,972
1,762
I looked at it two ways ... Millman's and Superposition.

5/37ths is correct.

• ###### Calculations.png
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7. ### logearav Thread Starter Member

Aug 19, 2011
248
0
Thanks a lot everyone for your painstaking efforts to help me.