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# Norton Theorem

Any active network can be depicted as an equal current source with a parallel impedance linked across it. It is called Norton Theorem to simplify any network by converting the active portion of that network to an equal current source with a parallel linked impedance.

## What is Norton Theorem?

Norton Theorem is alternative of Thevenin Theorem. In this theorem, the circuit network is decreased to a single source of steady current in which parallel to it is attached the corresponding internal resistance. Each source of voltage can be transformed to an equal source of current.

Suppose we need to figure out the current through a specific branch in a complicated network. If there is one or more active sources in the network, they will provide the said branch with current.

As in the following branch current comes from the remaining of the network, the network itself can be classified as a current source. The network’s equivalent impedance across the branch is nothing but the impedance of the equivalent current source and is therefore parallel linked. A network’s equivalent resistance is the network’s electrical resistance equivalent when someone looks back from the terminals where that branch is connected back into the network. All sources are removed during the calculation of this equivalent resistance, leaving their internal resistance in the network. In fact, the branch of the network through which we need to figure out the current is removed from the network in Norton Theorem. We shorten the terminals where the said branch was attached after removing the branch.

Then we calculate the short circuit current that flows in the terminals. This current is Norton equivalent current IN of the source. The equivalent resistance between the said terminals with all sources removing leave their internal resistances in the circuit is calculated and say, it is RN. Now we will form a current source that’s internal shunt resistance is RN Ω and current is IN A.

We clarified it by the following example to get a clearer idea of this theorem.

Two resistances R1 and R2 are connected in series and this series combination is connected across one voltage source of internal resistance Ri and emf E. As shown, the series combination of one RL resistive branch and another R3 resistance is linked through the R2 resistance. Now, by implementing Norton Theorem, we need to figure out the current through RL.

First, we must remove the resistance RL from terminals A and B and shorten the terminals A and B by zero resistance.

Second, the short circuit current or equal Norton current IN must be calculated through points A and B.

The equivalent resistance,

To determine the network’s internal resistance or Norton equivalent resistance RN, remove the branch between A and B and exchange the original of voltage with its internal resistance. Now the equivalent resistance viewed from terminals A and B is RN,

According to Norton Theorem, the network acts as a source of constant current IN with shunt connected internal resistance RN when resistance RL is reconnected across terminals A and B and this is Norton equivalent circuit.