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

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 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. Under this condition the unknown resistance is given by X=MP/N.

Part A

If the galvanometer G shows zero deflection when M = 850.0 ? , N = 14.00 ? , and P = 33.58 ? , what is the unknown resistance X?

Express your answer with the appropriate units.

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 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. Under this condition the unknown resistance is given by X=MP/N.

Part A

If the galvanometer G shows zero deflection when M = 850.0 ? , N = 14.00 ? , and P = 33.58 ? , what is the unknown resistance X?

Express your answer with the appropriate units.

Explanation / Answer

When the voltages at each terminal of the galvanometer are equal and it indicates 0,

then the two voltage dividers

formed by M&s and P&X have equal division ratios and X/P = M/s thus X = PM/S.

X = 33.58*850/14 = 2038.78 ohm

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