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 R1 = 56.00 ,R2 = 140.0 , R3 = 150.0 , and R4 = 340.0 .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 . What is the resistance of the unknown resistor?

Explanation / Answer

first we calculate the equivalent resistance of R1 nd R2 . first block
As they are in parallel,R_eq1 = R1*R2/(R1+R2) = 56*140/(56+140) = 40 ohms

for second block ,with 4 resistors, we calculate the equivalent resistnce
first R1 +R3 = 56 +150 = 206 ohms, R2 + R4 = 140 + 340 = 480 ohms
R_eq2 = 206*480/(206+480) = 144.14
hence resistane between a and b = 200 ohms
200 = R_eq1 + R_eq2 +R5
200 = 40 + 144.14 + R5
R5 = 15.86 ohms

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