The Wheatstone bridge is a circuit used to measure unknown...

The Wheatstone bridge is a circuit used to measure unknown resistances. The bridge in the figure is balanced-no current flows through the galvanometer $\mathrm{G}$ (a sensitive detector of current whose operation is based on magnetic forces). (a) What is the unknown resistance $R_{x} ?[$ Hint: What is the potential difference between points $A$ and $B ?]$ (b) Do the resistance of the galvanometer or the internal resistance of the emf affect the measurement? Explain.

The Wheatstone bridge is a circuit used to measure unknown resistances. The bridge in the figure is balanced-no current flows through the galvanometer $\mathrm{G}$ (a sensitive detector of current whose operation is based on magnetic forces).
(a) What is the unknown resistance $R_{x} ?[$ Hint: What is the potential difference between points $A$ and $B ?]$ (b) Do the resistance of the galvanometer or the internal resistance of the emf affect the measurement? Explain.

Key Concepts

Wheatstone Bridge

The Wheatstone bridge is a circuit configuration used for precise measurement of an unknown resistance by comparing it with known resistances. It consists of four resistive arms arranged in a diamond shape. By adjusting the known resistances and achieving balance, the unknown resistance can be calculated using the ratio of resistances in the two arms.

Balanced Bridge (Null Condition)

The balanced condition, or null condition, is reached when no current flows through the galvanometer or detector, indicating that the potential difference between the two midpoints of the circuit is zero. This condition ensures that the ratios of the resistances in one branch are equal to the ratios in the other branch, which is critical for accurately determining the unknown resistance.

Ohm’s Law and Potential Division

Understanding Ohm’s Law and the concept of potential division is key to the Wheatstone bridge. When the bridge is balanced, the voltage drop across each leg is proportionate to its resistance, allowing the unknown resistance to be determined by setting up an equality between the voltage drops. This concept is critical in deriving the relationship used to calculate the unknown resistance.

Instrumental Effects and Measurement Accuracy

In a balanced bridge, the measurement is minimally affected by the internal resistance of the power source (emf) and the resistance of the galvanometer. Since no current flows through the detector at balance, the potential reading is not influenced by these additional resistances, making the method highly accurate for resistance determination.

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