# Superposition Problem with Four Voltage and Current Sources

Determine $V_x$ and $I_x$ using the superposition method.

Solution
I. Contribution of the $-5V$ voltage source:

To find the contribution of the $-5V$ voltage source, other three sources should be turned off. The $3V$ voltage source should be replaced by short circuit. The current source should be replaced with open circuits, as shown below.

It is trivial that $I_{x1}= \frac{-5 V}{2 \Omega}=-2.5 A$ . The current of the $3\Omega$ resistor is zero. Using KVL, $-(-5V)+V_{3\Omega}-V_{x1}=0 \to V_{x1}=-(-5V)=5V$ .

II. Contribution of the $3V$ voltage source:
Similarly, the $-5V$ voltage source becomes a short circuit and the current source should be replaced with open circuits:

The current of the $2\Omega$ resistor is zero because of being short circuited. It is trivial that $I_{x2}= 0 A$ (current of an open circuit). The current of the $3\Omega$ resistor is also zero. Using KVL, $-(3V)+V_{2\Omega}+V_{x2}+V_{3\Omega}=0 \to V_{x2}=3V$ .

III. Contribution of the $-1A$ current source:
The voltage sources should be replaced by short circuits and the $2A$ current source becomes with open circuit:

Again, the $2\Omega$ resistor is short circuited and its current is zero. it is clear that $I_{x3}= 1 A$ . The current of the $3\Omega$ resistor is equal to $-1A$ . Using KVL, $V_{x3}+V_{3\Omega}=0 \to V_{x3}+(-1A)\times (3\Omega)=0 \to V_{x3}=3V$ .

IV. Contribution of the $2A$ current source:
Likewise, the voltage sources should be replaced by short circuits and the $-1A$ current source becomes with open circuit:

Again, the $2\Omega$ resistor is short circuited and its current is zero. it is also trivial that $I_{x4}= 0A$ . The current of the $3\Omega$ resistor is $2A$ . Using KVL, $V_{x4}+V_{3\Omega}=0 \to V_{x4}+(2A)\times (3\Omega)=0 \to V_{x4}=-6V$ .

V. Adding up the individual contributions algebraically:

$V_x=V_{x1}+V_{x2}+V_{x3}+V_{x4}=5V+3V+3V-6V\to V_x=5V$
$I_x=I_{x1}+I_{x2}+I_{x3}+I_{x4}=-2.5A+1A+0A-0A\to I_x=-1.5A$

## 14 thoughts on “Superposition Problem with Four Voltage and Current Sources”

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