Question

The circuit shown in $\textbf{Fig. P26.74}$, 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 $S_1$ and $S_2$ 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 $\Omega$, $N =$ 15.00 $\Omega$, and $P =$ 33.48 $\Omega$, what is the unknown resistance $X$?

Name: Problem 74, Chapter 26: University Physics with Modern Physics
Uploaded: 2020-11-13T11:34:23-08:00
Duration: 8 min 23 s
Channel: Mohammad Amin

   The circuit shown in $\textbf{Fig. P26.74}$, 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 $S_1$ and $S_2$ 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 $\Omega$, $N =$ 15.00 $\Omega$, and $P =$ 33.48 $\Omega$, what is the unknown resistance $X$?

University Physics with Modern Physics

Hugh D. Young 14th Edition

Chapter 26, Problem 74

Instant Answer

Solved by Expert Mohammad Amin

11/13/2020

Step 1

This means that the voltage across the resistors M and X is the same, and the voltage across the resistors N and P is the same. We can write these conditions as follows: \[I_1M = I_2X \tag{1}\] \[I_1N = I_2P \tag{2}\] where $I_1$ is the current through resistors Show more…

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The circuit shown in $\textbf{Fig. P26.74}$, 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 $S_1$ and $S_2$ 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 $\Omega$, $N =$ 15.00 $\Omega$, and $P =$ 33.48 $\Omega$, what is the unknown resistance $X$?