Unknown value of added resistor in parallel

[grantaere]

Homework Statement

Picture provided.
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 = 14.00 Ω, R2 = 142.00 Ω, and R3 = 24.00 Ω. The voltage is V = 11 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.

Homework Equations

parallel circuit: 1/R = 1/(1/R1 + 1/R2)
series circuit: R = R1+R2
parallel: Vtotal = V1 = V2
series: Vtotal = V1 + V2
V = IR

The Attempt at a Solution

I tried finding the total resistance of the circut when switches are open, then using that with total voltage (11V) to find the current that goes through each resistor in series. (0.06111A) Then I used V = IR to find the voltage drops across each resistor in the series circuit. (V1 = 0.8555, V2=8.67777, V3=1.4666)
Then, I tried finding the resistance of R + R1 when the switches are closed-- R in parallel with R1-- and setting that equal to Vtotal/total current going through the juncture... but it gives me zero as an answer which is obviously wrong. Any hints would be very appreciated! I'm also quite confused as to how the outside switch factors into the problem at all.

 

[phinds]

You need to draw the circuit with the switches both open and write the loop equations, then draw the circuit with the switches both closed and write the loop equations. After that, I'll bet something will occur to you. :)

 

[lightgrav]

you already know that I1=0.06666A and V1=0.8555V ... the only other voltage (closed switches) is V2.
(once you determine a V, you can find a new I)

 

[grantaere]

Okay, so I tried drawing the second circuit (with switches closed) and found that R3 becomes zero since it's in parallel with a wire (assuming this is true?). In this case, I tried making the new total voltage = 11 = IR(2) + IR(unknown + 1 in parallel). Since it says the current remains the same across the R1 juncture regardless of whether the switches are closed, I assumed the current remains 0.06111A, and found the R in parallel to equal 3.8 ohm. Plugging that into 1/(1/R1 + 1/R) = R(parallel) I got the unknown R to equal 5.2ohm... but apparently this is still incorrect. What am I doing wrong?

 

[phinds]

I suggest, again, that you do what I suggested in post #2