The Wheatstone Bridge. The circuit shown in Fig. P26.74, called a Wheatstone bridge, is used to determine the value of an unknown resistor X by comparison with three resistors M, N, and P whose resistances can be varied. For each setting, the resistance of each resistor is precisely known. With switches S1 and S2 closed, these resistors are varied until the current in the galvanometer G is zero; the bridge is then said to be balanced. (a) Show that under this condition the unknown resistance is given by X = MP/N. (This method permits very high precision in comparing resistors.) (b) If galvanometer G shows zero deflection when M = 850.0 Ω, N = 15.00 Ω, and P = 33.48 Ω, what is the unknown resistance X?
Figure P26.74
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