The circuit shown in (Figure 1), called a Wheatstone bridge, is used to determin

Question

The circuit shown in (Figure 1), 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 S_1 and S_2 closed, these resistors are varied until the current in the galvanometer G in zero; the bridge is then sold to be balanced. Under this condition the unknown resistance is given by X = MP/N. If the galvanometer G shows zero deflection when M = 880.0 Ohm, N = 14.00 Ohm, and P = 33.58 Ohm, what is the unknown resistance X? Express your answer with the appropriate units.

Explanation / Answer

The given circuit is a wheatstone circuit and the uknown resistance in a balanced wheatstone bridge is given by:

X/P = M/N

X = MP/N

X = 860 x 33.58/14 = 2062.77 Ohm

Hence, X = 2062.77 Ohm

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