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Find the current through $1\Omega$ resistance using Mesh Analysis.

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Calculate VTH

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In Mesh I

(12+12) I1- 12 I2=24

24 I1- 12I2=24…………………. (1)

In Mesh II

-12 I1+ (12+10+4+12) I2=-32

-12 I1+38 I2=-32………………….. (2)

I1=0.6875 A, I2=-0.625A

Apply KVL to ABA

-VAB +32+ (12+4) I2=0

32+16(-0.625) = VAB

VTH= VAB22V

→ Calculation of RTH

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$12Ω|| 12Ω=6Ω \hspace{3cm} 4Ω+12Ω=16Ω$

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$$16Ω||16Ω=8Ω \\ RTH=8Ω$$

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