Good day ! I am a physics student and not an EE so I'm quite hesitant with approaching this circuit problem. What will be the equations for this analysis? Will their be current in the red line even though the given voltages are V1 = 20V and V2 = 10V. Will V1 not overpower V2?

Two voltage sources in a circuit

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    \$\begingroup\$ No, they will not overpower because they are not in parallel because R1 is there. \$\endgroup\$ – DKNguyen Apr 14 at 21:22
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    \$\begingroup\$ This is not a homework solution service. We expect you to demonstrate that you have made a substantial effort to solve this yourself, show all of your work, and then ask a specific question. The answer to your only real question is yes, there will be current. What techniques do you know that you can apply to this? \$\endgroup\$ – Elliot Alderson Apr 14 at 21:22
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    \$\begingroup\$ Assume your bottom node is "zero" (you are allowed to do that.) Then the upper left node is known as \$V_1\$ and the upper right node is known as \$V_2\$. Since you know the voltage across \$R_1\$ (as a difference I'm sure you can work out) you can work out its current. Since you know the voltage across \$R_2\$ you can also work out its current. If there is a difference between these currents, then \$V_2\$ handles it. What's left to do? \$\endgroup\$ – jonk Apr 14 at 21:24
  • \$\begingroup\$ These are not parallel. Such a problem is easily solved by superposition. Can be solved even easier if you have some intuition about it. \$\endgroup\$ – Eugene Sh. Apr 14 at 21:26
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    \$\begingroup\$ Electrical engineering is physics; it's just a very specialized branch. Show us how far you've gotten. \$\endgroup\$ – TimWescott Apr 14 at 21:30

You won't get far with intuitions like "Will V1 not overpower V2". You should approach such problems with rigorous equations.

First, you should find all "nodes", these are parts that are connected with ideal wires (lines) and thus have the same potential (voltage). In this case, there are three nodes: the bottom part; top-left between V1 and R1; and top-right part between R1 R2 V2.

Then you have to call one of these nodes "0 volts". Because the voltage is difference of potentials, you first have to have some reference. (it is like measuring altitude, you can tell differences easyly, but to have absolute values you need some "zero level" first)

The choice of the node with 0V potential is arbitrary, but I recommend selecting the one where the "-" of the power supply is (if the circuit is that simple).

Now, try to find voltages of all other nodes. In this case, you already know them: top left is 0V+V1=20V, top right is 0V+V2=10V.

IR1 and I? (red arrow) are marked towards the node and IR2 is heading away from it. It makes intuitive sense that whatever goes in must get out, so IR1+I?=IR2. Note, that direction of current may no be the same as the arrow. The arrow marks positive direction. If the current is flowing opposite to the arrow, it will be negative number. Always check minus signs in circuit calculations. It may be misleading to assume what the direction of current will be. Just mark one direction and result will be either positive or negative.

Now you just need IR1 and IR2. You know nodes voltages, so you know voltage across resistors and calculating current is trivial. But remember to check sign: if the current is marked from higher voltage to lower, it will be positive. Otherwise negative. (that holds for components that draw power, oposite holds for power sources)

The current will be (10V-0V)/R2 - (20V-10V)/R1

There aren't exact values for R1 and R2 provided. If R1 was smaller than R2, the result would be negative number (so current flows opposite to the red arrow, in the source). This would be valid solution, it just means that V2 source is drawing power instead of supplying it (could be accumulator that is charging. In circuit analysis it simply means there is heat generated).

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    \$\begingroup\$ Re, 'you have to call one of these nodes "0 volts"' Might be worth mentioning that if you see a diagram with a ground symbol, that means the person who drew the diagram chose that node to be the 0 Volt node. And, if you want to take it a step further, you could mention that whenever there's more than one ground symbol, then they're all implicitly tied together. \$\endgroup\$ – Solomon Slow Apr 15 at 1:04
  • \$\begingroup\$ Thank you! There was no R values provided I'm assuming because it's just an example to help us work in theory for circuit analysis. \$\endgroup\$ – taylor-series Apr 15 at 6:31
  • \$\begingroup\$ Please don't provide answers to obvious homework problems. The OP needed a nudge, and you provided that, thank you. But don't feel like you need to press on and provide the complete and final answer. This site will be flooded with homework questions if we do that. \$\endgroup\$ – Elliot Alderson Apr 15 at 11:43

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