Superposition Question, electric circuits

[string_656]

Homework Statement

^^^^ = resistor = 10 ohm
<> = 3*Vab Dependent voltage. (the voltage equals 3 times Vab)
0 = voltage source 4 v (inderpendant)
o = Inderpendant Current source 2 A



|--^^^^---<>---------a +
| + + - |
0 o Vab
| - |
|-----------------------b -

Question asks, Find Vab (the voltage across a and b) using superposition

Homework Equations

Well there's lots, ohms, KCL, KVL etc,

The Attempt at a Solution

I want to attempt it, but i don't no how to break this down, as all the examples in the txt book don't have the dependant votlage source, and in the examples they are solving for a voltage across a resistor.

Any ideas? thanks
ps i also uploaded the image just incase the one above didnt work once posted

 

[CEL]

What is the current through the 10 ohm resistor?
What are the voltages at the two ends of this resistor?

 

[Mene]

my response would be as follows:

Superposition is a powerful tool that allows us to analyze complex systems by breaking them down into simpler parts. In this case, we can use superposition to solve for Vab by considering the effects of each source individually.

First, we can consider the effect of the voltage source alone by setting the current source to 0 A. This results in a simple circuit with a series connection of a 4 V voltage source and a 10 ohm resistor. Using Ohm's law, we can calculate the voltage across the resistor as 4 V. This voltage is equal to Vab since there are no other elements in the circuit.

Next, we can consider the effect of the current source alone by setting the voltage source to 0 V. This results in a circuit with a parallel connection of the 10 ohm resistor and the dependent voltage source. Using Kirchhoff's Current Law, we can calculate the current through the dependent voltage source as 2 A. This current is equal to 3 times Vab, so Vab must be equal to 2/3 V.

Finally, we can combine these two results using the principle of superposition. This states that the total voltage across Vab is equal to the sum of the voltages calculated in each individual case. Therefore, Vab = 4 V + 2/3 V = 14/3 V.

In summary, by using superposition, we were able to solve for Vab by considering the effect of each source individually and then combining the results. This method can be applied to more complex circuits as well, making it a valuable tool for circuit analysis.