Nodal analysis produces a compact set of equations for the network, which can be solved by hand if small, or can be quickly solved using linear algebra by computer.
Because of the compact system of equations, many circuit simulation programs (e.g. When elements do not have admittance representations, a more general extension of nodal analysis, modified nodal analysis, can be used. Even though the nodes cannot be individually solved, we know that the combined current of these two nodes is zero.
The branch currents are written in terms of the circuit node voltages.
As a consequence, each branch constitutive relation must give current as a function of voltage; an admittance representation.
$$I_ = \frac$$ $$\Rightarrow I_ = 2A$$ Therefore, the current flowing through 20 Ω resistor of given circuit is 2 A.
Note − From the above example, we can conclude that we have to solve ‘n’ nodal equations, if the electric circuit has ‘n’ principal nodes (except the reference node).
Find the current flowing through 20 Ω resistor of the following circuit using Nodal analysis.
Step 1 − There are three principle nodes in the above circuit.
Follow these steps while solving any electrical network or circuit using Nodal analysis.
Now, we can find the current flowing through any element and the voltage across any element that is present in the given network by using node voltages.