The Wheatstone bridge. The circuit shown in Fig. P26.81. called a wheatstone bri

Question

The Wheatstone bridge. The circuit shown in Fig. P26.81. called a wheatstone bridge, is used to determine the value of an unknown  resistor X by comparison with three resistor M,N, and P whose resistances can be varied. For each setting, the resistance of each resistor is precisely known. With Switches K1 and K2 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 the galvanometer G shows zero deflection when M=850.0 ohms, N=15.00 ohms and P=33.48 ohms, what is the unknown resistance X?

The Wheatstone bridge. The circuit shown in Fig. P26.81. called a wheatstone bridge, is used to determine the value of an unknown resistor X by comparison with three resistor M,N, and P whose resistances can be varied. For each setting, the resistance of each resistor is precisely known. With Switches K1 and K2 closed, these resistors are varied until the current in the galvanometer G is zero; the bridge is then said to be balanced. Show that under this condition the unknown resistance is given by X=MP/N. (This method permits very high precision in comparing resistors.) If the galvanometer G shows zero deflection when M=850.0 ohms, N=15.00 ohms and P=33.48 ohms, what is the unknown resistance X?

Explanation / Answer

The Wheatstone bridge. The circuit shown in Fig. P26.81. called a wheatstone bri

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