Question

state and prove Thevenin's Theorem​

Answer 1

Thevenin's Theorem

Any combination of batteries and resistances with two terminals can be replaced by a single voltage source e and a single series resistor r. The value of e is the open circuit voltage at the terminals, and the value of r is e divided by the current with the terminals short circuited.

Proof of Thévenin’s theorem for an example

Before we do the general proof let’s do this specific example,

We are interested in what’s happening at the 2 kΩ2\,\text k\Omega2kΩ resistor on the far right, so we identify the port by drawing the two little port circles. Our goal is to simplify the rest of the circuit (everything to the left of the port) by finding its Thévenin equivalent. Here’s the circuit we’re going to transform, with the 2 kΩ2\,\Omega2kΩ resistor removed,

To demonstrate Thévenin’s theorem we need to show the voltage at the port can be written in the form v=VT−i RT\goldC v = \text V_\text T - \blueD i\,\text R_\text Tv=VT−iRT, where VT\text V_\text TVT and RT\text R_\text TRT are to be discovered.

The demonstration is pretty clever. We use the the principle of superposition. Whenever you see multiple sources, superposition should pop into your head.