Using the Mesh Equation Technique and Cramers Rule find the

Using the Mesh Equation Technique and Cramer\'s Rule, find the current, IL, for the circuit given in Figure #2. Label all clockwise currents on the schematic.

Solution

consider left side current as i1

consider right side loop current as i2

apply kvl to left side loop

-60+10i1+10(i1-i2)+30=0

2i1-i2=3

apply kvl to right side loop

20i2+30i2-30+10(i2-i1)=0

-i1+6i2=3

from the above equations

i1=1.909 amps

i2=0.818 amps

current through left side 10 ohms resistor=i1=1.909 amps

current through middle 10 ohms resistor=(i1-i2)=1.091 amps

current through 20 ohms and 30 ohms resistors=i2=0.818 amps