A multiloop circuit is shown in the figure Find the currents

A multiloop circuit is shown in the figure. Find the currents I_2, I_2, I_2, I_4 and the Voltages E_1 and E_2.

Solution

Apply Kirchoff\'s second law to adeba loop you get ,

24 = 13 i1 +5(5)+3(2)

    = 13 i1 +25 +6

    =13 i1 + 31

13 i1 = 24-31

        = -7

   i1 = -7/13 = -0.5384 A

Apply Kirchoff\'s second law to degfd loop you get , 5(5)= 20 -E1

E1 = 20 -25 = -5 volt

Apply Kirchoff\'s seond law to bchgec loop you get ,

E2-20 = -4(i3)+3(2)

   E2 = -4i3 +6 +20

        = -4i3 +26      ---------( 1)

Apply Kirchoff\'s second law to abchgfda loop you get ,

-24 +E2 -E1 = -4 i3 -13 i1

-24 +E2 -(-5) = -4 i3 -13 ( -0.5384)

-19 +E2 = -4i3 + 7     ---------------------( 1)

Apply Kirchoff\'s first law to junction e you get ,

5 A = 2 A + i2

   i 2 = 5A-2A= 3A

Apply Kirchoff\'s first law to junction d you get ,

5 A +i4 = i1

           = -0.5384 A

        i4 = 5.5385 A

Apply Kirchoff\'s first law to junction g you gte , i3 = i4 + i2

i3 = 5.5385 +3

      = 8.5385 A

Substitute this value in equation( 1) you get ,

-19 +E2 = -4(8.5385) + 7

             = -27.154

       E2 = -27.154 +19

            = -8.154 volt