Norton's theorem is an important method used to simplify electrical circuits. It states that any linear two-terminal network of voltage sources, current sources and resistances can be replaced by an equivalent circuit consisting of a single current source in parallel with a single resistance. The application of Norton's theorem to a circuit yields a Norton equivalent circuit ā a current source (called the Norton current, I_N) in parallel with a resistance (called the Norton resistance, R_N). This makes it much easier to find the current through any one load connected to the terminals.
Norton's theorem replaces a linear two-terminal network with a current source in parallel with a resistance.
Applying Norton's theorem to a circuit yields a Norton equivalent: I_N in parallel with R_N.
Norton current I_N = the short-circuit current across the two terminals.
Norton resistance R_N = the equivalent resistance with all sources deactivated.
Load current: I_L = I_N Ć R_N / (R_N + R_L) (current-divider rule).
Norton resistance equals Thevenin resistance: R_N = R_Th.
Norton and Thevenin equivalents are duals: I_N = V_Th / R_Th.
Norton's theorem states: 'Any linear, bilateral two-terminal network containing voltage sources, current sources and resistances can be replaced by an equivalent circuit consisting of a current source (I_N) in parallel with a resistance (R_N), connected across the two terminals.'
Here: ā¢ I_N (Norton current) = the current that would flow through the two terminals if they were short-circuited. ā¢ R_N (Norton resistance) = the equivalent resistance of the network seen from the two terminals when all sources are deactivated (voltage sources short-circuited and current sources open-circuited).
So, the application of Norton's theorem to a circuit yields a simple current source I_N in parallel with a resistance R_N.
Step 1: Remove the load resistor (the part of the circuit through which you want to find the current) from the two terminals.
Step 2: Find the Norton current (I_N): short-circuit the two open terminals and calculate the current flowing through this short circuit.
Step 3: Find the Norton resistance (R_N): deactivate all independent sources (replace voltage sources with a short circuit and current sources with an open circuit) and find the equivalent resistance looking back into the terminals.
Step 4: Draw the Norton equivalent circuit ā the current source I_N in parallel with R_N.
Step 5: Reconnect the load resistor (R_L) across the terminals and find the load current using the current-divider rule: I_L = I_N Ć R_N / (R_N + R_L)
Norton's theorem is closely related to Thevenin's theorem; they are 'duals' of each other.
ā¢ Thevenin equivalent: a voltage source V_Th in series with a resistance R_Th. ā¢ Norton equivalent: a current source I_N in parallel with a resistance R_N.
The relations between them are: ā¢ R_N = R_Th (the equivalent resistance is the same in both) ā¢ I_N = V_Th / R_Th ā¢ V_Th = I_N Ć R_N
A Thevenin equivalent can always be converted to a Norton equivalent and vice versa, using source transformation.
Norton's theorem states that any linear two-terminal network containing voltage sources, current sources and resistances can be replaced by an equivalent circuit consisting of a current source (Norton current, I_N) in parallel with a resistance (Norton resistance, R_N) connected across the terminals.
The application of Norton's theorem to a circuit yields a Norton equivalent circuit ā that is, a single current source (I_N) in parallel with a single resistance (R_N). This simplified circuit can then be used to easily find the current through any load connected across the terminals.
The Norton current (I_N) is found by short-circuiting the two output terminals and calculating the current through that short circuit. The Norton resistance (R_N) is found by deactivating all independent sources (short-circuiting voltage sources and open-circuiting current sources) and calculating the equivalent resistance seen from the terminals.
Norton's and Thevenin's theorems are duals of each other. The Norton equivalent is a current source I_N in parallel with R_N, while the Thevenin equivalent is a voltage source V_Th in series with R_Th. They are related by R_N = R_Th and I_N = V_Th / R_Th, and one can be converted to the other by source transformation.
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