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Use mesh analysis to find current through 10Ω in the ckt shown
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Applying clockwise current in two meshes,

Applying Kirchhoff's Voltage Law to Mesh 1

$-10I_1-25+15-15(I_1-I_2)=0\\ 25I_1-15I_2=-10...................(1)$

Mesh 2 contains a current source of 5 A. Hence we can write current equation for Mesh 2. Since direction of the current source and the mesh current I2 are opposite, 

$I_2=-5....................(2)$

Solving equations (1) and (2), 

$I_1=-3.4\ A\\ I_{10\Omega }=I_1=-3.4\ A$

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