Consider the DC circuit shown in Fig. 4. The 3 currents I_1, I_2, & I_3 are unkn

Question

Consider the DC circuit shown in Fig. 4. The 3 currents I_1, I_2, & I_3 are unknown. In order to find them, Kirchhoff's rules must be used to find 3 algebraic equations which can be used to solve for the 3 unknowns. a. Apply Kirchhoff's junction rule at point c to derive a simple relationship between the 3 currents. This is one of the equations needed to solve for the 3 unknown currents. b. Apply Kirchhoff's loop rule to the loop labeled abcda to derive a second equation needed to solve for the 3 unknown currents. c. Apply Kirchhoff's loop rule to the loop labeled befcb to derive a third equation needed to solve for the 3 unknown currents. d. Using the three equations derived in parts a, b, & c, calculate (find numerical values for) the 3 currents I_1, I_2, & I_3.

Explanation / Answer

Lets write the three kirchoff's equations

-16 + 8I1 -12 -6I2 = 0

12 - 8I1 - 4I3 = 0

I3 = I1 + I2

8I1 -6I2 = 28

12I1 +4I2 = 12

I1 = 23/13

I2 = -30/13

I3 = -7/13

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