Norton’s Theoram Notes

Where as Thevenin’s theorem was used to simplify a network to a constantvoltage source and a series resistance. Norton’s theorem can be used to resolve a
network into a constant-current source and a parallel resistance. The interchange of voltage sources and current sources by use of Thevenin’s and Norton’s theorems
is sometimes useful in circuit analysis.
The theorem may be stated as follows :
Statement : Any combination of linear bilateral circuit elements and active sources, regardless of the connection or complexity, connected to a given load Rl can be replaced by a simple two terminal network, consisting of a single current source of IN amperes and a single impedance RTH in parallel with it, across the
two terminals of the load RL. The In is the short circuit current flowing through the short circuited path, replaced instead of. It is also called Norton’s current. The
RTH is the equivalent impedance of the given network as viewed through the load  terminals, with RL removed and all the active sources arc replaced by their internal
impedances. If the internal impedances are unknown then the independent voltage sources must be replaced by short circuit while the independent current sources
must be replaced by open circuit, while calculating RTH.

Steps to Apply Norton’s Theorem

Step 1: Short the branch through which the current is to be calculated.

Step 2: The current through this short circuited branch, using any of the nets simplification techniques. This current is Norton’s current IN.

Step 3: Calculate the equivalent resistance RTH, as viewed through the terminals ol interest, by removing the branch resistance and making all the independent source;
inactive.

Step 4: Draw the Norton’s equivalent across the terminals of interest, showing a cuisource with the resistance RTH parallel with it

Step 5: Reconnect the branch resistance. Let it be RL. Then using current division in parallel circuit of two resistances, current through the branch of interest can be
obtained as.