Find the Current and potential difference in a parallel/series circuit

[Absolutism]

Homework Statement

Okay. I got two different answers for these and I don't know which one is right so I could continue from there. If you will please help by letting me know which answer is right and why, I'd very much appreciate it.

This is the figure:
http://www.webassign.net/pse/p28-09alt.gif
where R = 20ohm

1. Find the current in R (20ohm resistor)
2. Find the potential difference between points a and b

Homework Equations

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The Attempt at a Solution

Answers I got:

One says that the first 3 resistors on the top are all in parallel, and then the total of that is in series with the other two that have 20 and 5 ohm, so the total is 27.5

The other answer is that in the resistor at the very top, the current goes through the wire then meets a junction and separates into say, i1, i2, i3 and then they all meet again at the junction near point a. So the bottom 2 resistors are in series, but then the total of that and the two resistors above it are all in parallel, then in series with the very top one.
So we have 1/25+1/10+1/5
then r= 2.94
added to 10
so 12.94

If you could please let me know which one is on the right track, I'd appreciate it.

 

[gneill]

This is the figure:
http://www.webassign.net/pse/p28-09alt.gif

...Page not found

edit: ...Okay, now page is found.

 

[gneill]

Your second version is on the right track, and the value you obtained for the total equivalent resistance is good (although units are not specified. Always specify units!).

 

[Absolutism]

Okay. Thank you so much. I'll continue it now. I thought I was making stuff up at some point!

 

[Nickie]

Hello,

Thank you for reaching out for assistance. I would like to provide you with some clarification on the concepts of current and potential difference in a parallel/series circuit.

Firstly, in a parallel circuit, the current splits up and flows through multiple branches, while in a series circuit, the current flows through each component in a single path. In your given circuit, the current will split into three branches at the junction before reaching point a.

Now, let's look at the first answer you provided. It states that the first 3 resistors on the top are all in parallel, and then the total of that is in series with the other two resistors. This is incorrect. In a parallel circuit, the total resistance is always less than the resistance of the individual branches. This means that the total resistance in this circuit would be less than 20 ohms, not 27.5 ohms. Additionally, the resistors in the bottom two branches are not in series, as the current splits up at the junction before reaching point a.

Moving on to the second answer, it correctly identifies that the bottom two resistors are in series, but then adds the total resistance of those two branches to the resistance of the top resistor. This is incorrect, as the top resistor is in parallel with the other three resistors. In a parallel circuit, the total resistance is calculated using the equation 1/Rtotal = 1/R1 + 1/R2 + 1/R3, where Rtotal is the total resistance and R1, R2, and R3 are the individual resistances in the parallel branches. In this case, the total resistance would be less than 10 ohms, not 12.94 ohms.

To find the current in the 20 ohm resistor, we can use Ohm's law, which states that current (I) is equal to voltage (V) divided by resistance (R). In this case, the voltage across the 20 ohm resistor is the same as the voltage across the 10 ohm and 5 ohm resistors, which is equal to the potential difference between points a and b. So, the current in the 20 ohm resistor would be (Vab/20) = (10/20) = 0.5 amps.

To find the potential difference between points a and b, we can use Kirchhoff's voltage law, which states that the sum