Thevenin’s theorem and Norton’s theorem - fundamental concepts in electrical engineering

Thevenin's Theorem and Norton's Theorem are fundamental concepts in electrical engineering used to simplify complex circuits, making it easier to analyze current and voltage in circuits.

Thevenin's Theorem:

Thevenin's Theorem states that any linear circuit with voltage and current sources and resistances can be replaced at a specific pair of terminals by an equivalent single voltage source (V_Thevenin) in series with a resistance (R_Thevenin). To find the Thevenin equivalent:

1. Identify the portion of the circuit you want to replace with the Thevenin equivalent and the terminals across which you will calculate this equivalent.
   
   
2. Remove the load resistance if there is any across the terminals, then calculate the open-circuit voltage across these terminals, which gives you V_Thevenin.
   
   
3. Next, to find R_Thevenin, deactivate all independent voltage sources (replace them with a short circuit) and all independent current sources (replace them with an open circuit). Calculate the equivalent resistance seen from the terminals.

Norton's Theorem:

Norton's Theorem is similar to Thevenin's Theorem. It states that any linear circuit with voltage and current sources and resistances can be replaced at a specific pair of terminals by an equivalent current source (I_Norton) in parallel with a resistance (R_Norton). To find the Norton equivalent:

1. Identify the portion of the circuit you want to replace with the Norton equivalent and the terminals across which you will calculate this equivalent.
   
   
2. Remove the load resistance if there is any across the terminals, then calculate the short-circuit current across these terminals, which gives you I_Norton.
   
   
3. To find R_Norton, follow the same procedure as you would for finding R_Thevenin—deactivate all independent sources and calculate the equivalent resistance seen from the terminals. Note that R_Norton is equal to R_Thevenin.

Both theorems are powerful tools in circuit analysis because they simplify the process of analyzing power systems, especially when determining the effect of varying loads.