Find v in electric circuit (nodal analysis, superposition)

[The_Lobster]

Homework Statement

Find the voltage v across the 5 Ohm resistor as shown in the attached drawing.

Homework Equations

Ohm's law, V=IR

The Attempt at a Solution

I have done plenty of these using different techniques, superposition/source transformation, nodal or mesh analysis, etc. But what puts me off with this one is that I don't really see where I should start. Am I right that I cannot turn the current source on the left into a voltage source because the two resistors in parallel have a node in between them?

What I have done so far is to devise two equations for the current in the two loops two the right of the drawing, disconnecting the current source (superposition), and I get: (I_1 = upper mesh)
Upper mesh:
$$0 = -9V + 35 I_1$$
Lower mesh:
$$0 = 9V + 15I_2$$

If I know put the current source back in place, and remove the voltage source, how would I then proceed to find the current through the 5 ohm resistor from th ecurrent source?

 

[The Electrician]

Replace the 9 volt source with a short; then the 20 and 15 ohm resistors will be in parallel and can be replaced with their equivalent. The 10 and 5 ohm resistors are similarly in parallel and can be replaced with a single equivalent. Solve that circuit for the voltage across the equivalent resistors. Now backtrack; you know the voltage across each parallel combination, and you can easily calculate the current in each resistor that makes up the combinations because you know the voltage across them.

 

[The_Lobster]

Thank you!

But what about the contribution from the voltage source once we put that back?

 

[The Electrician]

This is superposition.

You calculate the contribution from the current source with the voltage source shorted, and add that to the contribution from the voltage source with the current source open circuited.

 

[DeeNos]

I would suggest approaching this problem by first identifying the nodes in the circuit and labeling them. Then, using the nodal analysis technique, you can write a KCL equation for each node to solve for the unknown voltages. In this case, you can start with the node between the two parallel resistors and write an equation for the current leaving the node. Since there is only one unknown voltage at this node, you can solve for it.

After that, you can use superposition to find the voltage across the 5 ohm resistor by considering the contributions from each source separately. First, consider the current source alone and use Ohm's law to calculate the voltage across the 5 ohm resistor. Then, do the same for the voltage source alone. Finally, add these two values to get the total voltage across the resistor.

Overall, it is important to approach this problem systematically and break it down into smaller, more manageable steps. By using nodal analysis and superposition, you can easily find the voltage across the 5 ohm resistor in this circuit.