Electrical Engineering Circuit Theorems and Conversions

Kirchhoff's Current Law (KCL) states that the total current entering a junction (or node) in an electrical circuit is equal to the total current leaving the junction. Mathematically, it is expressed as: ∑Iin=∑Iout\sum I_{in} = \sum I_{out}∑Iin​=∑Iout​

Kirchhoff's Voltage Law (KVL) states that the sum of the electrical potential differences (voltage) around any closed loop or mesh in a circuit is zero. Mathematically, it is expressed as: $\sum V=0$

Ohm's Law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R). The formula is: $V=I\times R$ It is significant in circuit analysis for determining the relationship between voltage, current, and resistance in electrical circuits.

Thevenin's Theorem states that any linear electrical network with voltage sources and resistances can be replaced by an equivalent circuit consisting of a single voltage source (Thevenin voltage) in series with a single resistance (Thevenin resistance). This simplifies complex circuit analysis.

To find Thevenin’s equivalent circuit:

1. Remove the load resistor from the original circuit.
2. Calculate Thevenin Voltage (V_th): Find the open-circuit voltage across the terminals where the load was connected.
3. Calculate Thevenin Resistance (R_th): Turn off all independent sources (replace voltage sources with short circuits and current sources with open circuits) and find the resistance between the open terminals.
4. Re-draw the circuit with V_th in series with R_th and reattach the load resistor.

Norton’s Theorem states that any linear electrical network with voltage sources and resistances can be replaced by an equivalent circuit consisting of a single current source (Norton current) in parallel with a single resistance (Norton resistance).

To find Norton’s equivalent circuit:

1. Remove the load resistor from the original circuit.
2. Calculate Norton Current (I_N): Find the short-circuit current across the terminals where the load was connected.
3. Calculate Norton Resistance (R_N): Same as Thevenin Resistance (turn off all independent sources and find the resistance between the open terminals).
4. Re-draw the circuit with I_N in parallel with R_N and reattach the load resistor.

The Superposition Theorem states that in any linear circuit with multiple independent sources, the response (voltage or current) in any branch of the circuit is the algebraic sum of the responses caused by each independent source acting alone, with all other independent sources turned off (replaced by their internal impedances).

To apply the Superposition Theorem:

1. Select one independent source and turn off all other independent sources (replace voltage sources with short circuits and current sources with open circuits).
2. Analyze the circuit and determine the output (voltage or current) due to the selected source.
3. Repeat the process for each independent source.
4. Sum the individual contributions from each source to find the total response

The Maximum Power Transfer Theorem states that maximum power is delivered to the load when the load resistance (R_L) is equal to the Thevenin resistance (R_th) of the source network providing the power.