How do you calculate the Thevenin resistance?

Identify the circuit: Determine the circuit for which you want to find the Thevenin resistance. It should be a linear circuit containing independent sources (voltage or current sources) and resistors.

Remove the load: Disconnect any load (resistor or any other component) connected across the terminals where you want to find the Thevenin resistance. This open circuit will be the "load condition" for the Thevenin equivalent circuit.

Find the open-circuit voltage (Voc): Using any suitable circuit analysis method (e.g., nodal analysis, mesh analysis, superposition, etc.), find the voltage across the open terminals of the circuit. This voltage is the Thevenin voltage (Vth) and represents the voltage when the load is disconnected.

Short-circuit the voltage sources: Replace all voltage sources in the original circuit with a short circuit. This effectively sets their voltage to zero and keeps only the resistors and current sources.

Find the short-circuit current (Isc): Using the same analysis method as in step 3, determine the current flowing through the short-circuited terminals (the current source, if any, will contribute to this current). This current is the Thevenin current (Ith) and represents the current when the load is replaced with a short circuit.

Calculate the Thevenin resistance (Rth): Divide the Thevenin voltage (Vth) by the Thevenin current (Ith):

Rth = Vth / Ith

The resulting value of Rth is the Thevenin resistance, which is the equivalent resistance seen from the open terminals of the circuit when the load is removed. It represents the resistance of an ideal voltage source connected in series with this resistance, which can replace the original circuit when connected to the same load.

Keep in mind that this method works only for linear circuits, which means circuits obeying Ohm's law and where the current-voltage relationship of each element remains constant. Non-linear elements, such as diodes and transistors, require different methods to find Thevenin equivalents.