A Wheatstone bridge measures an unknown resistance by balancing two legs of a circuit. It consists of four resistors arranged in a diamond shape, with a power source and a galvanometer connected between the junctions. By adjusting the known resistances until the galvanometer reads zero (indicating no current flow), the ratio of the known resistances can be used to calculate the unknown resistance using the formula ( R_x = \frac{R_2}{R_1} \times R_3 ). This method allows for precise measurement of the unknown resistance without direct current flow through it.
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