Electronic – KCL Node Analysis

The book says that I1 is traveling through the 8 ohm resistor (R1) towards ground. But when I build the circuit on multi-sim it says that I1 is traveling through (R1) upwards "clockwise. I'm confused why the book says I1 is counter clockwise and my simulator says clockwise. ... I always seem to be confused on how to determine the direction of the current.

You don't need to know the direction of the current before you solve the circuit. You can guess whichever way you want. If the current is actually flowing the other way, you'll just get a negative number for the value of the current.

The book says that I1 is traveling through the 8 ohm resistor (R1) towards ground. But when I build the circuit on multi-sim it says that I1 is traveling through (R1) upwards "clockwise.

In the example in the book, what was the value they found for I1? If it was negative, there's no contradiction with the simulation result.

You can solve this circuit by more or less the same method you've given in the question; however you need to plug in one more equation (\$V_1=V_2+12\$) into the system and introduce an unknown current variable. So I'm not sure if we can call it a 'pure' nodal analysis.

This is what you've got to do:

• Write KCL on the left node (\$I_s\$ is the current through the voltage source): $$6A=\frac { { V }_{ 1 }-{ V }_{ 2 } }{ { R }_{ 3 } } +\frac { { V }_{ 1 } }{ { R }_{ 3 } } +{ I }_{ s }$$

• Do it again on the node on the right side: $$4A={ I }_{ s }-\frac { { V }_{ 2 } }{ { R }_{ 2 } } +\frac { { V }_{ 1 }-{ V }_{ 2 } }{ { R }_{ 3 } } $$

• So far, we're in line with the method described in the question. As a last step, write down this one: $$V_1=V_2+12$$

Now we're left with 3 equations in three unknowns, which you can easily solve to get \$V_1, V_2\$ and \$I_s\$