Basic DC Theory
KIRCHHOFF’S LAWS
Solution:
Figure 36 Using the Current Law
First, apply Kirchhoff’s voltage law to both loops.
Loop ABCDEF
Loop ABGHEF
IR = Esource
IR = Esource
2 Itotal + 6 I1 = 6
2 Itotal + 3 I2 = 6
Since Kirchhoff’a current law states Itotal = I1 + I2, substitute (I1 + I2) in the place of Itotal in both
loop equations and simplify.
Loop ABCDEF
Loop ABGHEF
2 (I1 + I2) + 6 I1 = 6
2 (I1 + I2) + 3 I2 = 6
2 I1 + 2 I2 + 6 I1 = 6
2 I1 + 2 I2 + 3 I2 = 6
8 I1 + 2 I2 = 6
2 I1 + 5 I2 = 6
We now have two equations and two unknowns and must eliminate I1 to find I2. One way is to
multiply Loop ABGHEF equation by four, and subtract Loop ABCDEF equation from the result.
Multiply by 4:
4 (2 I1 + 5 I2 = 6)
8 I1 + 20 I2 + 24
Rev. 0
Page 47
ES-02
