Briefly explain Thevenin's theorem ?

Thevenin's theorem states that any linear electrical network can be replaced by an equivalent circuit consisting of a single voltage source in series with a single resistor. This equivalent circuit, known as the Thevenin equivalent circuit, has the same voltage-current characteristics as the original network when connected to any external load. This theorem simplifies the analysis of complex circuits by reducing them to simpler equivalent circuits.

Thevenin's Theorem:

Thevenin's theorem states that any linear circuit containing a single source of electrical energy and resistors can be replaced by an equivalent circuit consisting of a voltage source Vth in series with a resistor Rth connected across a load resistor.

Equivalent Circuit:

- Voltage Source (Vth): The open-circuit voltage of the original circuit, measured with the load resistor open.
- Resistor (Rth): The resistance of the original circuit with the voltage source turned off (replaced by a short circuit).

Derivation:

Thevenin's theorem is based on the superposition principle and the fact that the current through the load resistor in the original and equivalent circuits is the same. By setting up the appropriate equations, the equivalent source values can be derived:

- Vth = Vab (open circuit)
- Rth = R_equivalent (source off)

Uses:

Thevenin's theorem is useful for:

- Simplifying complex circuits for analysis
- Finding the power delivered to a load
- Determining the maximum power transfer condition