Find the Norton's equivalent current source I_N, if the following circuit is converted into equivalent Norton's circuit:

Norton Theorem

Norton's theorem states that it is possible to simplify any linear circuit, into an equivalent circuit with a single current source and a parallel resistance.

Steps to calculate:

1. Norton Resistance (RN): Open the circuit to the terminal from where the Norton resistance has to be found. While finding the RN, short circuit the independent voltage source and open circuit the independent current source.
2. Norton Current (IN): This is the short-circuit current across the terminals where the load was connected.

Calculation

The short circuit path will make 6Ω resistance ineffective.

Applying KCL at node V:

\({V-15\over 3}-4+{V\over 3}=0\)

2V = 27

V = 13.5 volts

The current across 3Ω resistance is given by:

\(I_N={13.5\over 3}=4.5\space A\)