The balanced condition of a Wheatstone bridge circuit occurs when the ratio of the resistances in one branch is equal to the ratio in the other branch, specifically when ( \frac{R_1}{R_2} = \frac{R_3}{R_4} ). Under this condition, the voltage across the galvanometer is zero, indicating no current flows through it. This balance allows for precise measurements of unknown resistances by comparing them to known resistances. The bridge circuit is often used in applications such as strain gauges and temperature sensors.
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