Wheatstone Bridge

A Wheatstone bridge is a null measurement device that measures unknown resistance by balancing potential drops across circuit branches. It comprises two parallel branches with four resistors connected by a galvanometer. The variable resistor is adjusted until the galvanometer reads zero, indicating no current flows through it and the circuit is balanced. This allows calculation of the unknown resistance using the ratio of known resistance values.

A galvanometer acts as a bridge between the two parallel branches of the circuit, detecting when current flow stops. When the galvanometer reads zero deflection, it indicates that junction points have equal potential and no current flows through the bridge. This null condition is essential for accurate resistance measurement, as it allows the unknown resistance to be calculated from the balanced potential drops without drawing current from the circuit.

Balance occurs when the variable resistor is tuned until the galvanometer reads zero. At this point, the potential at junction points b and d becomes equal, meaning the potential drop across R1 equals the drop across R3, and the potential drop across R2 equals the drop across Rx. This balanced state indicates no current flows through the galvanometer, allowing accurate calculation of the unknown resistance from the known resistance values.

A Wheatstone bridge is more accurate than standard ohmmeters because it uses a null measurement technique that draws no current from the circuit. Standard ohmmeters using voltmeters or ammeters alter the voltage applied and current flow, reducing accuracy. The Wheatstone bridge's balanced condition eliminates these measurement errors, providing precise resistance values when the galvanometer shows zero deflection.

Two significant factors affect Wheatstone bridge accuracy. First, achieving exactly zero current through the galvanometer is impossible in real circuits; some residual current always flows. Second, uncertainty in the known resistance values directly contributes to uncertainty in calculating the unknown resistance. These combined factors limit the precision of the measurement despite the bridge's superior design compared to standard resistance-measuring devices.

The Wheatstone bridge consists of two parallel branches containing four resistors, with a galvanometer connecting the branches as a central bridge element. Unlike standard parallel circuits, the galvanometer acts as a null detector rather than a load. When balanced, both branches receive the same potential drop from the voltage source, and the bridge configuration allows measurement of unknown resistance through the ratio of known resistances.

When the Wheatstone bridge is balanced, the ratio of potential drops yields an expression for the unknown resistor. Since the potential drop across R1 equals the drop across R3, and the potential drop across R2 equals the drop across Rx, taking the ratio of these equations produces a formula expressing the unknown resistance in terms of the three known resistance values in the circuit.