Using the superposition theorem, find V_x in the following circuit.

Concept :

Superposition Theorem

Superposition theorem states that in any linear, active, bilateral network having more than one source, the response across any element is the sum of the responses obtained from each source considered separately and all other sources are replaced by their internal resistance. The superposition theorem is used to solve the network where two or more sources are present and connected.

The internal impedances of Independent sources are replaced as follows

•             Replacing all other independent voltage sources with a short circuit

•             Replacing all other independent current sources with an open circuit

Calculations :

1.When 20 V Source Is Acting Alone

Applying KCL

$\frac{V_x-20}{20}+\frac{V_x}{4}=0.1V_x$

V_x (0.05 + 0.25 - 0.1) = 1

V_x = 5 V

2.When 4 A Source Is Acting Alone

Applying KCL,

0.1V_x + 4 = V_x /4 + V_x / 20

V_x  = 20 V

Total response when both sources acting is the sum of responses when individual sources acting alone

V_x = V_x1 + V_x2 = 5 + 20 = 25 V