Find the Thevenin's voltage V_th across 2-ohm resistance.

Concept:

Thevenin's Theorem:

Any two terminal bilateral linear DC circuits can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.

To solve Problems with independent Sources:

To find Voc: Calculate the open-circuit voltage across load terminals. This open-circuit voltage is called Thevenin’s voltage (Vth).

To find Rth: 

To calculate Thevenin’s Resistance we should replace all independent current sources with an Open circuit and Independent voltage sources with a Short circuit.

Application:

Let 2 Ω be the Load of the given circuit and open circuit to get Thevenin voltage.

A circuit diagram can be drawn as

By applying KVL,

9 - 4I - 4I - 6I = 0

\(I=\dfrac{9}{4+4+6}=\dfrac{9}{14}\ A\)

\(V_{th}=4I=4\times \dfrac{9}{14} =2.57\ V\)