(Wheatstone bridge) Show that if Rx / R3=R1 / R2 in the...

(Wheatstone bridge) Show that if $R_{x} / R_{3}=R_{1} / R_{2}$ in the figure, then $I=0 .(R_{0}$ is the resistance of the . instrument by which $I$ is measured.) This bridge is a method for determining $R_{x^{\prime}} . R_{1}, R_{0}, R_{3}$ are known. $R_{3}$ is variable. To get $R_{n}$ make $I=0$ by varing $R_{3}$ Then calculate $R_{B}=R_{2} R_{1} / R_{2}$.

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Key Concepts

Wheatstone Bridge

The Wheatstone bridge is an electrical circuit used to accurately measure an unknown resistance by balancing two legs of a circuit composed of four resistors. It works by comparing the ratios of resistances in two parallel branches until the potential difference across a central detector (usually a galvanometer) becomes zero, indicating that the bridge is balanced.

Bridge Balance Condition

The bridge balance condition is achieved when the ratio of resistances in one branch equals the ratio in the other branch. Under this condition, the voltage difference across the detector becomes zero, meaning no current flows through it. This crucial condition enables the calculation of the unknown resistance solely from the known resistors in the circuit.

Resistive Network Proportionality

This concept involves understanding the proportionality relationships in a network of resistors. In a balanced Wheatstone bridge, the equality of the ratios of resistors (i.e., Rx/R3 = R1/R2) ensures that the potential drops across the arms of the bridge are proportionate. This proportionality is key for determining the unknown resistance by setting up and solving ratio equations.

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