For the circuit shown in the figure below, we wish to find the currents I1, I2,

Question

For the circuit shown in the figure below, we wish to find the currents I1, I2, I3. Use Kirchhoff's rules to complete the equation for the upper loop.(Use any variable or symbol stated above as 30V= Use Kirchhoff's rules to complete the equation for the lower loop.(Use any variable or symbol stated above as -24V= Use Kirchhoff's rules to obtain an equation for the junction on the left side.(Use any variable or symbol stated Solve the junction equation for I3. I3= Using the equation found in part (d), eliminate I3 from the equation found in part(b).(Use any variable or symbol st 24V= Solve the equation found in part(a) and part (e) simultaneously for the two unknowns for I1 and I2, respectively. I1= I2= Substitute the answers found in part (f) into the junction equation found in part (d), solving for I3. I3=

Explanation / Answer

a) 12-7I2-5I1+18-8I1-11I2=0 (going anticlockwise)

=>30=13I1+18I2................(1)

b) 36+7I2-12+11I2-5I3=0 (going anticlockwise)

=>-24=18I2-5I3..............(2)

e) I3=I2+I1

so from (2) we have -24=18I2-5(I2+I1)=-5I1+13I2

=>24=5I1-13I2...................(3)

f) From (1) we have

I2=(30-13I1)/18

From (2) we have

24=5I1-13(30-13I1)/18

=>432=90I1-390+169I1

=>822=259I1

=>I1=3.174 A

I2=(30-13I1)/18

=>I2=-0.625 A

g)I3=I2+I1

=>I3=3.174-0.625

=>I3=2.549 A

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