Calculate the magnitude f current through 3 ohm resistor in the circuit applying Kirchoff's laws.indicate the direction of current through 3 ohm resistor.

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Please find below the solution to the asked query:

For the loop  1(left one) we have assumed current in clockwise sense i1while current in loop 2 is i2 in anticlockwise sensewriting loop equation for loop 1:we have 42 -6i1 -3(i1 +i2) = 0or 42 = 9i1 +3i2....(1)writing loop equation for loop 2:we have, -10 -4i2 -3(i1 +i2) = 0or, 10 = -3i1 -7i2....(2)solving equation 1 and 2, we have multiply equation(1) by 7 and equation  (2)by 3 and add both of themwe have294 = 63i1 +21i2 ...(3)30 = -9i1 -21i2 ... (4)adding (3) and (4)294 +30 = 54i1or i1  = 6 amperenow substituting  i1  = 6 ampere  in equation (2) we have i2 = -10 +3i1 7 = -4 ampere, the negative sign implies that the assumed current is in opposite direction of the actual current.

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