Batman is attempting to defuse a bomb created by The Riddler and opens it to fin

Question

Batman is attempting to defuse a bomb created by The Riddler and opens it to find a set of resistors connected as shown in the figure below. He can tell from the coloring on several of the resistors that some are equivalent to each other, and he determines that = 58.00 0, R2 = 125.0 0, R3 = 150.0 0, and R4 = 315.0 0. However, he needs to know the resistance of R5 before he can begin defusing the bomb. Using his Bat-Ohm-Meter, he is able to determine that the equivalent resistance between points a and b is 200.0 ohm. What is the resistance of the unknown resistor?

Explanation / Answer

start from left,
R1 and R2 are in parellel. Their equivalent resistance be R'
R' = (R1*R2)/(R1+R2)
= (58*125)/(58+125)
=39.62 ohm

(R1+R3) is in parallel with (R2+R4). Their equivalent resistance be R''
R'' = (R1+R3)*(R2+R4) / (R1+R2+R3+R4)
= (58+150)*(125+315)/(58+125+150+315)
   =141.2 ohm
  
R',R'' and R5 are in series
Req = R' + R'' + R5
200 = 39.62 + 141.2 + R5
R5 = 19.18 ohm

Answer: 19.18 ohm

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