KCL to Find Voltage Between a and b

[Gbox]

Homework Statement

Find the voltage between a and b

2. Homework Equations
KVL, KCL

The Attempt at a Solution

[/B]
I did not understand how they have reach the result we just two equations, and how did they use KCL to get those equations

 

[gneill]

There are only two essential nodes in the circuit, and they are labeled v and v_oc. The node at the top of the 20 V supply is not an essential node since its potential with respect to the reference node is fixed by that voltage source. Effectively that node's potential is already "solved".

Since there are only two essential nodes, only two node equations are required in order to completely analyze the circuit.

The KCL equations that were written are node equations. They sum the currents at a given node. Look at them term by term and you should recognize the currents for each branch leading into a given node.

 

[Gbox]

Why is the node on top on the 20V is "solved"? There are different currents coming out of it?

 

[gneill]

Why is the node on top on the 20V is "solved"? There are different currents coming out of it?

Nodal analysis determines the potentials at the nodes with respect to the reference node. The potential at that node is already known: 20 V.

Given the node potentials the potential difference across every branch in the circuit can be determined, hence the currents can be determined, too, by Ohm/s law.