Wheatstone Bridge - Operation

Operation

In the figure, is the unknown resistance to be measured;, and are resistors of known resistance and the resistance of is adjustable. If the ratio of the two resistances in the known leg is equal to the ratio of the two in the unknown leg, then the voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer . If the bridge is unbalanced, the direction of the current indicates whether is too high or too low. is varied until there is no current through the galvanometer, which then reads zero.

Detecting zero current with a galvanometer can be done to extremely high accuracy. Therefore, if, and are known to high precision, then can be measured to high precision. Very small changes in disrupt the balance and are readily detected.

At the point of balance, the ratio of

\begin{align} \frac{R_2}{R_1} &= \frac{R_x}{R_3} \\ \Rightarrow R_x &= \frac{R_2}{R_1} \cdot R_3
\end{align}

Alternatively, if, and are known, but is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of, using Kirchhoff's circuit laws (also known as Kirchhoff's rules). This setup is frequently used in strain gauge and resistance thermometer measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.

Read more about this topic:  Wheatstone Bridge

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