Norton’s theorem states that any linear electrical network with voltage and current sources and resistances can be replaced by an equivalent circuit containing a current source (IN) in parallel with a resistor (RN). This equivalent circuit is valid for any load connected to the network terminals. Essentially, it’s a way to simplify complex circuits into more manageable forms for analysis.
To solve a circuit using Norton’s theorem, follow these steps:
- Identify the Load: Determine the part of the circuit for which you want to find the Norton equivalent.
- Remove the Load: Disconnect the load from the circuit. This leaves the terminals of the circuit open.
- Calculate the Norton Current (IN): To find the Norton current, short-circuit the terminals of the load and calculate the current flowing through this short circuit. This current is the Norton current.
- Calculate the Norton Resistance (RN): To find the Norton resistance, deactivate all independent sources (voltage and current) in the original circuit. Then, determine the equivalent resistance looking into the terminals of the circuit.
- Construct the Norton Equivalent Circuit: Once you have (IN) and (RN), create the Norton equivalent circuit by placing a current source (IN) in parallel with a resistor (RN).
- Reconnect the Load: Reconnect the original load to the terminals of the Norton equivalent circuit.
- Analyze the Circuit: You can now analyze the circuit with the simplified Norton equivalent to determine the desired quantities, such as voltage, current, or power.
Step: 1
Step: 2
Step: 3
\[\color{red}{I=\frac{E}{R_t}}\]
\[\color{red}{R_t=R_1+\frac{R_2\times R_3}{R_2+R_3}}\]
\[\color{red}{I_N=\frac{R_3}{R_2+R_3}\times I}\]
Step: 4
\[\color{red}{R_N=R_2+\frac{R_1\times R_3}{R_1+R_3}}\]
Step: 5
\[\color{red}{I_L=\frac{R_N}{R_N+R_L}\times I_N}\]
