What is the value of R3 in the circuit given?

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In the circuit analysis discussion, the values for resistors R1 and R2 are given as 1 ohm and 10 ohms, respectively, with known currents I1 and I4. The power dissipated by R4 is calculated to be 5 ohms. The confusion arises around R3, which is initially misunderstood as potentially being in series with R2 and R4, but is clarified to be in parallel with them. After applying Kirchhoff's Current Law (KCL) and analyzing the circuit, it is determined that R3 is 20 ohms based on the voltage across it and the current flowing through it. The discussion emphasizes the importance of correctly interpreting circuit diagrams and applying fundamental electrical principles.
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Homework Statement



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In the circuit shown, R1 = 1 ohms, R2 = 10 ohms, I1 = 3.5 A and I4 = 2 A. The battery has negligible internal resistance. If the rate at which R4 is dissipating electrical energy is 20W:

a) What is R4
b) What is R3
c) What is I3
d) What is the emf of the battery?

Homework Equations


The Attempt at a Solution



I solved for a:
P = (I4)R R4
20 W = 4 R4
R4 = 5 ohms.

Now I am stuck there. Honestly, I don't know what the R3 illustration means. I know that R2 and R4 are parallel to each other. But the R3 which is like a diagonal confuses me. What does that R3 mean? And how do I go about to solve this?

Does the R3 mean that it connects the R2 and R4, which makes them in series? I am reallly confused and I don't have a book to consult this to.
 
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Don't let diagonal lines fool you; Connections are connections no matter how the lines are drawn on paper.
 
I still don't get it. The answer to R3 should be 20 ohms. But I can't think of any solution that will lead to that.
 
Start by labeling your diagram with everything you know or can determine so far. That would include indicating given currents and component values, as well as any voltage drops you can determine from the given resistances and currents. Find the current that must be flowing through R3 and the voltage that must be across it.
 
If it helps to imagine that R3 is straight up and down then do so, the resistors R2, R3, and R4 are all in parallel and no matter how it is drawn the laws governing them remain the same.
 
I really can't understand this.. I tried this:

If R3 is parallel to R2.

R23 = R2R3 / R2+R3 = 10R3 / 10+R3
I23 = I2 + I3 = 1 + I3
V23 = V2 = 10V = V3

Is that right? What should I do next?
 
Did you label your diagram with all the currents you know? Can KCL help you to find I3?
 
Oh in that case, I found I3 to be 0.5A.

Thus, R3 = V3 / I3
R3 = 10 / 0.5 = 20 ohms

Thanks!
 

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