A Wheatstone bridge is a type of \"bridge circuit\" for making precise measureme

Question

A Wheatstone bridge is a type of "bridge circuit" for making precise measurements of an unknown resistance. The unknown resistance to be measured is R_x, which is placed in the circuit with accurately known resistances R_1, R_2, and R_3 (see the figure). R_3 is a variable resistor and it is adjusted so that when the switch is closed momentarily, the ammeter A shows zero current flow. That is, R_3 adjusted until points B and D are brought to the same potential, as there is no current flowing through the ammeter once the switch is closed.

Explanation / Answer

From Figure we can say,
I3 = Ix
I1 = I2

I3 * R3 = I1 * R1
Ix * Rx = I2* R2

Rx = I2*R2/Ix
Rx = I2*R2/I3
Rx = I2*R2/(I1*R1)/R3
Rx = R3 * (I2*R2) / (I1*R1)

We know,
I2 = I1 SO,

Rx = R3 * (R2/R1)
Hence Proved.

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