Electrical Circuit Theorems: Superposition

Superposition Theorem:

The superposition theorem is a fundamental principle in electrical engineering and circuit analysis. It states that In a linear circuit with multiple independent sources (such as voltage and current sources), each independent source acting alone causes a response (voltage or current) in any component, and the overall response is the algebraic sum of these individual responses. To apply the superposition theorem, one must:

1. Focus on one independent source at a time, and replace the remaining sources with their internal impedances by using short circuits for voltage sources and open circuits for current sources.
2. Calculate the contribution of each source to the response in the component of interest.
3. Sum the individual contributions to find the total response.

The superposition theorem simplifies the analysis of complex circuits by allowing the study of one source at a time and is applicable only to linear circuits where the principle of linearity (homogeneity and additivity) holds true.

Electrical Circuit Theorems: Thevenin

Thevenin Theorem:

Thevenin’s Theorem is a fundamental principle in electrical engineering and circuit analysis, named after the French engineer Léon Charles Thévenin. It simplifies the analysis of complex linear electrical circuits, making it easier to study and understand the behavior of a particular component within the circuit.

According to Thevenin’s Theorem, you can simplify any linear electrical network, consisting of voltage sources, current sources, and resistances, into a single voltage source (Thevenin voltage, VthV_{th}Vth​) in series with a single resistance (Thevenin resistance, RthR_{th}Rth​), and connect it to a load.

The steps to apply Thevenin’s Theorem are as follows:

1. Identify the portion of the circuit to be analyzed: Remove the load resistor where you want to determine the current or voltage.
2. Determine Thevenin voltage ((V_{th})): Measure the open-circuit voltage at the terminals where the load was connected.
3. Determine Thevenin resistance ((R_{th})): Replace all independent voltage sources with short circuits and independent current sources with open circuits, then calculate the equivalent resistance seen from the open terminals.
4. Reconstruct the Thevenin equivalent circuit: Connect the calculated Thevenin voltage ((V_{th})) in series with the Thevenin resistance ((R_{th})), and then reconnect the load resistor to this simplified circuit.

By reducing a complex circuit to a simple Thevenin equivalent, the analysis of the circuit’s response to various loads becomes straightforward, allowing for easier calculations and better insight into the circuit’s behavior.

Norton Theorem:

Norton’s Theorem is a key concept in electrical engineering and circuit analysis, named after the American engineer Edward Lawry Norton. It allows for the simplification of complex linear electrical circuits, facilitating the analysis of a particular component within the circuit.

Norton’s Theorem states that you can reduce any linear electrical network with voltage sources, current sources, and resistances to an equivalent circuit consisting of a single current source (Norton current, INI_NIN​) in parallel with a single resistance (Norton resistance, RNR_NRN​), connected to a load.

The steps to apply Norton’s Theorem are as follows:

1. Identify the portion of the circuit to be analyzed: Remove the load resistor where you want to determine the current or voltage.
2. Determine Norton current ((I_N)): Calculate the short-circuit current that flows between the open terminals where the load was connected.
3. Determine Norton resistance ((R_N)): Replace all independent voltage sources with short circuits and independent current sources with open circuits, then calculate the equivalent resistance seen from the open terminals.
4. Reconstruct the Norton equivalent circuit: Connect the calculated Norton current ((I_N)) in parallel with the Norton resistance ((R_N)), and then reconnect the load resistor to this simplified circuit.

Norton’s Theorem simplifies complex circuits, similar to Thevenin’s Theorem, by making it easier to analyze circuit responses to various loads. The Norton equivalent circuit is especially useful for parallel components and can be converted to a Thevenin equivalent through source transformation.

Maximum power transfer theorem: The power transferred from a supply source to a load is maximum when the resistance of the load is equal to the internal resistance of the source. 

Magnetic circuits: The screw rule gives the direction of the magnetic flux lines.