Find the currents in the circuit shown SolutionLet the curre

Find the currents in the circuit shown.

Solution

Let the current in top is \"i\" and the current in middle is i \' and bottomis i \"

Apply kirchoff\'s second law to upper loop you get ,

12 = 10 i \' + 5 i + 20 i

12= 10 i \' + 25 i       --------( 1)

Apply kirchoff\'s second la to bottom loop you get ,

6 = 5 i \" -10 i \'       -----------( 2)

But from kirchoff\'s first law , i = i \' + i \"

                                        i \" = i - i \'

Substitute this in equation(2) you get,

6 = 5(i-i\') -10 i \'

   = 5 i -5 i \' -10 i \'

6 = 5 i -15 i \'           -----------( 3)

From equation (2) , 12= 25 i +10 i \' ----------( 4)

equation(4) -(equation(3) x5) ==>

12 -(6x5) = 25 i +10 i \' -5(5i-15i\')

     12 -30 = 25 i +10 i\' -25 i +75 i \'

                 = 85 i \'

           -18 = 85 i \'

               i \' = -0.2117 A

Substitute i \' value in equation(3) you get ,

6 = 5 i -15(-0.2117)

   = 5 i + 3.176

5i = 2.823

i = 0.564 A

Therefore i \" = i - i\'

                   = 0.564A-(-0.2117 A)

                   = 0.564A+0.2117 A

                   = 0.7764 A