This is a question about the soluiton to Problem 26.74 in the University Physics

Question

This is a question about the soluiton to Problem 26.74 in the University Physics with Modern Physics textbook 14th edition.

In step 2, why is the voltage at b and c the same? I know Voltage is the same in parallel, but wouldn't that mean the voltage from a to d along resistors N and M is the same as the votage from a to d along resistors P and X?

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-MPN. IThis method permits very high precision in comparing resistors.) (b) If galvanometer G shows zero deflection when M 850.0 Q, N 15.00 2, and P 33.48 2, what is the unknown resistance X? Figure P26.74

Explanation / Answer

a) When wheat stone bridge is balanced

=> IN * N = IP * P

Also, IM * M = IX * X

Also, IN = IM

And, IP = IX

Thus, X = MP/N

b) unknown resistance X =   850 * 33.48/15

                                          = 1897.2 ohm

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