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I would like to solve for the unknown voltage and current \$V_x\$ and \$I_x\$. Below is the image of the circuit.

Should I first solve the current flowing in resistors 3 and 4 through equations of KVL and KCL and then solve the unknown values \$V_x\$ and \$I_x\$ through KCL? Can someone clarify on what should I do in this one?

enter image description here

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    \$\begingroup\$ hint: first, start labeling all the components with names R1, R2, ..., otherwise it will be impossible to discuss things like "voltage over that one resistor in the corner". then: if you know a resistance and the current that flows through it, you know the voltage across it. With that, you know one more voltage in a specific loop, and can caclulate the current across another resistor. \$\endgroup\$ Nov 9 '21 at 12:06
  • \$\begingroup\$ Nice, thanks for the labelling. so, have you figured out what you can do after considering \$I_2\$ and \$R_4\$? \$\endgroup\$ Nov 9 '21 at 12:22
  • \$\begingroup\$ oh wait, your labelling removed facts from your schematic, so now we don't know what is given and what needs to be found: maybe you'll want to add back in what values were already in there! \$\endgroup\$ Nov 9 '21 at 12:23
  • \$\begingroup\$ @MarcusMüller, after considering the \$R_4\$ and \$I_7\$, should I use KCL to find the unknown values \$V_x\$ and \$I_x\$? That is what I am thinking about and I am not sure if that is correct. I am also not sure but I am thinking that \$I_7\$ is not really the current flowing in \$R_4\$. \$\endgroup\$
    – Sigwasan
    Nov 10 '21 at 11:49
  • \$\begingroup\$ You can't directly infer \$V_x\$ at that point, but what about the voltage across \$R_3\$? When you have that, what about the current through it? What about the current through \$R_1\$ afterwards? As Elliot says, this is like solving a crosswords puzzle, or a sudoku, or playing solitaire: you solve one, then you get info about the next. \$\endgroup\$ Nov 10 '21 at 12:22
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Here is the basic approach:

  1. Look at the information you have. If you know the voltage across or current through a resistor, use Ohm's Law to find any missing value.

  2. Use KVL around any loops. If you have an equation with just one unknown, solve for it.

  3. Use KCL at all nodes. If you have an equation with just one unknown, solve for it.

Repeat this process until you have found all desired values. There is no magic bullet. You simply have to put in the effort to solve the problem.

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1)You can apply KCL at the negative terminal of V1 to find the current flowing through R2. Finding Vx then is just applying Ohm's law.

2)You can then apply KCL at the negative terminal of V2 to find the third current(two of them are known).

3)Finally you can apply KVL through the loop consisting of the two voltage sources to find out the current through R3. You can then use this to find the current Ix.

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