How do you calculate the Norton resistance?
1 Answer
To calculate the Norton resistance, you first need to understand what Norton's theorem is. Norton's theorem states that any two-terminal linear circuit containing voltage and current sources can be replaced by an equivalent circuit consisting of a current source in parallel with a resistor.
The Norton resistance, often denoted as "Rn," is the equivalent resistance of the original circuit as seen from the two terminals, with all voltage sources replaced by short circuits (ideal wires) and all current sources replaced by open circuits (gaps).
Here's a step-by-step guide on how to calculate the Norton resistance:
Disconnect all voltage sources in the original circuit.
Replace all current sources with an open circuit (a gap).
Identify the two terminals across which you want to find the Norton resistance.
Mark the terminals as "A" and "B."
Now, to calculate the Norton resistance (Rn):
Remove any load or resistor that might be connected across terminals A and B.
Short-circuit the terminals A and B by connecting them together using an ideal wire (a piece of wire with zero resistance).
Analyze the circuit and calculate the resulting short-circuit current flowing between terminals A and B. This current is the Norton current (In). You can use any circuit analysis method, such as Kirchhoff's current and voltage laws or mesh/nodal analysis, to find the short-circuit current.
Reopen the connection between terminals A and B (remove the short circuit).
Calculate the Norton resistance (Rn) using Ohm's law:
Rn = Voltage across A and B (Vab) / Norton current (In)
Since the terminals are short-circuited, the voltage Vab across them will be zero.
Therefore, Rn = 0 / In = 0
So, in conclusion, the Norton resistance (Rn) of the two-terminal circuit with all voltage sources replaced by short circuits and all current sources replaced by open circuits is always zero. This is because the current source in Norton's equivalent circuit model is in parallel with the resistance, and in this case, the resistance is effectively an open circuit (infinite resistance) due to the short circuit across the terminals.
The Norton resistance, often denoted as "Rn," is the equivalent resistance of the original circuit as seen from the two terminals, with all voltage sources replaced by short circuits (ideal wires) and all current sources replaced by open circuits (gaps).
Here's a step-by-step guide on how to calculate the Norton resistance:
Disconnect all voltage sources in the original circuit.
Replace all current sources with an open circuit (a gap).
Identify the two terminals across which you want to find the Norton resistance.
Mark the terminals as "A" and "B."
Now, to calculate the Norton resistance (Rn):
Remove any load or resistor that might be connected across terminals A and B.
Short-circuit the terminals A and B by connecting them together using an ideal wire (a piece of wire with zero resistance).
Analyze the circuit and calculate the resulting short-circuit current flowing between terminals A and B. This current is the Norton current (In). You can use any circuit analysis method, such as Kirchhoff's current and voltage laws or mesh/nodal analysis, to find the short-circuit current.
Reopen the connection between terminals A and B (remove the short circuit).
Calculate the Norton resistance (Rn) using Ohm's law:
Rn = Voltage across A and B (Vab) / Norton current (In)
Since the terminals are short-circuited, the voltage Vab across them will be zero.
Therefore, Rn = 0 / In = 0
So, in conclusion, the Norton resistance (Rn) of the two-terminal circuit with all voltage sources replaced by short circuits and all current sources replaced by open circuits is always zero. This is because the current source in Norton's equivalent circuit model is in parallel with the resistance, and in this case, the resistance is effectively an open circuit (infinite resistance) due to the short circuit across the terminals.