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I need help to solve this question, the first part was to solve for the missing currents which I have done, and the second part is to calculate each resistor value.

On the left is the circuit given on the right I've redrawn it to make it more easy to view.

I am struggling to know where to start: enter image description here

Apologies for the poor quality and hand-drawing!

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    \$\begingroup\$ 4 KCL nodes 4 KVL loops and only 5 unknowns hmmm \$\endgroup\$ Oct 24 at 16:55
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I think you managed to complete the first part of the question, which is to work out the specific currents through the devices. (I'd missed seeing your table at first as I tend to initially ignore someone's solution and instead focus on the diagrams and other information to gain an independent view of the situation.)

Let's redraw your schematic:

schematic

simulate this circuit – Schematic created using CircuitLab

Since you already used KCL to complete the currents in the above schematic, there's no point beating that idea for any further help.

But there's a problem.

While we know that \$V_{\!_\text{A}}\lt V_{\!_\text{B}}\$ and that \$0\:\text{V}\lt \left(V_{\!_\text{A}},V_{\!_\text{B}}\right)\lt 10\:\text{V}\$, that's about all we know for sure. We could pick any pair of node voltages for those two nodes, so long as the choices meet those requirements. Then, given that otherwise rather arbitrary pair of choices, just compute resistor values from there.

So, go ahead. Pick \$V_{\!_\text{A}}\$ and \$V_{\!_\text{B}}\$ such that \$V_{\!_\text{A}}\lt V_{\!_\text{B}}\$ and just compute resistor values. You have an infinity of options here.

Where exactly did you get this problem? Or is there another piece of information you didn't provide (or that I may have missed in reading your question?)

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