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.
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.