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Resistance in a Wheatstone bridge

A simple Wheatstone bridge has arms of R1 = 120 ohm, R2 =100 ohm and R3 =125 ohm. What is the value of R4 for balance? If R4 = 200 ohm and the bridge is driven with a source of 200 V. What is the open circuit voltage?

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Wheatstone bridge is a measuring instrument invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. It is used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer except that in potentiometer circuits the meter used is a sensitive galvanometer.

Here, Rx is the unknown resistance to be measured; R1, R2 and R3 are resistors of known resistance and the resistance of R2 is adjustable. If the ratio of the two resistances in the known leg (R2/R1) is equal to the ratio of the two in the unknown leg (Rx/R3), then the voltage between the two midpoints will be zero and no current will flow between the midpoints. R2 is varied until this condition is reached. The current direction indicates if R2 is too high or too low.

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