Electrical – Calculating the Thévenin Voltage (Vt) and Thévenin Resistance (Rt) equivalent of the circuit below

thevenin

How would one calculate the Thévenin voltage and Thévenin resistance for the circuit above?

Best Answer

Thevenin Voltage

The Thevenin voltage e used in Thevenin's Theorem is an ideal voltage source equal to the open circuit voltage at the terminals.

The 2 Ohm resistor is "open" and the 4 and 6 Ohm resistors form a voltage divider, therefore:

Vt = (50V * 6 Ohm) / ( 4 Ohm + 6 Ohm) =

300 / 10 = 30V

Explanation: The voltage at the node between the 3 resistors is the same proportion between the 6 Ohm resistor (which is the one attached to 0V) and the total resistance presented by the voltage divider (6 + 4 Ohm), so 6/10, 60%. 60% of 50V = 30V.

This can be better visualized this way:

schematic

^{simulate this circuit – Schematic created using CircuitLab}

Thevenin Resistance

The Thevenin resistance r used in Thevenin's Theorem is the resistance measured at terminals AB with all voltage sources replaced by short circuits and all current sources replaced by open circuits.

So:

Rt =

(6 Ohm in parallel with 4 Ohm) + 2 Ohm =

(6 * 4)/(6 + 4) + 2 = 24/10 + 2 = 4.4 Ohm

This can be better visualized this way:

schematic