Finding an Unknown Resistance

[Lamp Guy]

Homework Statement

The current going through the resistor R1 in the figure does not change whether the two switches S1 and S2 are both open or both closed. The resistances are R1 = 70.00 Ω, R2 = 50.00 Ω, and R3 = 62.00 Ω. The voltage is V = 15 V. With this information, what is the value of the unknown resistance R? Recall that a conducting wire can be treated as a resistor of 0 Ω, and points on a wire between resistors are at the same potential. Hint:
Kirchoff's rules are useful here.

The image is found here: http://www.chegg.com/homework-help/questions-and-answers/current-going-resistor-r1-figure-change-whether-two-switches-s1-s2-open-closed-resistances-q4890516

Homework Equations

R(for series)=R1+R2+R3
R(for parallel)=R1*R2/(R1+R2)

The Attempt at a Solution

I tried to add up all three resistors originally and got 182 ohms total, then made that equal to 50 + (70R)/(70+R) but it's not working. Not quite sure how to apply Kirchoff's rules here so any help would be appreciated.

 

[NascentOxygen]

Can you explain why you added up some resistor values? That will indicate whether you see the problem clearly.

You don't need Kirchoff's Laws, specifically. Ohm's Law will suffice. :)

 

[Lamp Guy]

I added them up because it said that the current is the same no matter what, so that's how I found the overall current.

 

[NascentOxygen]

I added them up because it said that the current is the same no matter what, so that's how I found the overall current.

Okay. That's with the switches in the positions shown? What numbers did you add? Did you do the addition in your head, or did you use a calculator?

 

[Lamp Guy]

i added 70, 50 and 62 to get 183.

 

[Lamp Guy]

182*

 

[NascentOxygen]

182*

Okay. (I was using the values on the figure.)

So that will allow you to calculate the current in R1? What value is it?

Next, how to determine R1's current with the switches closed?

 

[NascentOxygen]

... then made that equal to 50 + (70R)/(70+R) but it's not working. Not quite sure how to apply Kirchoff's rules here so any help would be appreciated.

What you are doing here is setting the battery currents equal, because you are equating the loop resistances. BUT the current through R1 is only a fraction of the battery current, with the switches closed.

So you have yet to find an expression for the current through R1 with switches closed. It would be a good idea to redraw the circuit as simply as possible, so you see clearly what is needed.

 

[Lamp Guy]

How do I find out what the current through R1 is? I thought that since it was parallel with the missing R, it would be 70R/(70+R). I've never worked with switches so I'm pretty confused by them.

 

[NascentOxygen]

How do I find out what the current through R1 is? I thought that since it was parallel with the missing R, it would be 70R/(70+R).

70R/(70+R) is the equivalent resistance of the parallel pair. Once you know the current through that pair then you need to sort out how much of it goes through each.

I've never worked with switches so I'm pretty confused by them.

That's why I suggested you redraw the circuit with the bare minimum necessary, for clarity. Draw it with no switches, etc.