Nodal Analysis With Current Source

Nodal Analysis With Current Source

      In nodal analysis provides a general procedure for analyzing circuits using node voltages as the circuit variables. In nodal analysis, we are interested in finding the node voltages. Given a circuit with n nodes without voltage sources, the nodal analysis of the circuit involves taking the following three steps.

Steps to Determine Node Voltages:

1. Select a node as the reference node. Assign voltages v2, p , vn -1
to the remaining n -1 nodes. The voltages are
referenced with respect to the reference node.
2. Apply KCL to each of the n-1 nonreference nodes. Use
Ohm’s law to express the branch currents in terms of node
voltages.
3. Solve the resulting simultaneous equations to obtain the
unknown node voltages.


The key idea to bear in mind is that, since resistance is a passive element, by the passive sign convention, current must always flow from a higher potential to a lower potential.

Example:

Determine the node voltages in the following circuit.

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Summing the currents INTO node A gives

1m - V_A / 4K + (V_B - V_A) / 8K = 0

Collecting terms and simplifying gives

3 V_A - V_B = 8   --------eq 1

Node B:

Summing the currents into node B gives

(V_A - V_B) / 8K - V_B / 16K - 2m = 0

Collecting terms and simplifying gives

2 V_A - 3 V_B = 32  --------eq 2 

Solving   eq1 and  eq2 just use metrix

V_A = - 1.143
V_B = - 11.43