Write equations for junctions a and e write equations for lo

Write equations for junctions a and e. write equations for loops abca, and cdec, and acea. Determine the direction and magnitude of the current in the horizontal wire between a and e.

Solution

At junction a ,I5 and I4 are enter into junction and I1 is leaving from a

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

I1 = I4 +I5

I1 -I4-I5 = 0

At junction e ,I3 is enter into junction and I5 and I2 are leaving from e

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

I3 = I2 +I5

I3 -I2-I5 = 0

(b).For abca loop

Apply Kirchoff\'s second law you get ,

E = R I1 +(4R) I4

For cdec loop

Apply Kirchoff\'s second law you get ,

-2E = -(2R) I2 -(3R) I4

2E = (2R) I2 +(3R) I4

For acea loop

Apply Kirchoff\'s second law you get ,

0 = -(4R) I4 +(3R) I3

(4R) I4 = (3R) I3

      I4 = (3/4)I3

(c). Give the values of R and E