Chapter 19, Problem 71GP

(a)

To determine

The value of unknown resistance in terms of known resistance.

Answer to Problem 71GP

The unknown resistance of the Wheatstone bridge in terms of known resistance is $\frac{R_2{R}_3}{R_1}$ .

Explanation of Solution

Given info:

The known resistance of the Wheatstone bridge are $R_1$ , $R_2$ and $R_3$ .

The unknown resistance of the Wheatstone bridge is, $R_x$ .

Formula Used:

The expression of balanced Wheatstone bridge is,

  $\frac{R_3}{R_x}=\frac{R_1}{R_2}$    ........(1)

Calculation:

Simplify the expression (1) to calculate the unknown resistance.

  $R_x=\frac{R_2{R}_3}{R_1}$

Conclusion:

Thus, the unknown resistance of the Wheatstone bridge in terms of known resistance is $\frac{R_2{R}_3}{R_1}$ .

(b)

To determine

The value of the unknown resistance.

Answer to Problem 71GP

The value of the unknown resistance is $71.28\Omega$ .

Explanation of Solution

Given info:

The value of first known resistance is, $R_1=630\Omega$ .

The value of second known resistance is, $R_2=972\Omega$ .

The value of third known resistance is, $R_3=46.2\Omega$ .

Formula Used:

The expression of balanced Wheatstone bridge is,

  $\frac{R_3}{R_x}=\frac{R_1}{R_2}$    ........(2)

Calculation:

Substitute all the values in the expression (2).

  $\begin{array}{c}\frac{46.2\Omega }{R_x}=\frac{630\Omega }{972\Omega }\\ R_x=71.28\Omega \end{array}$

Conclusion:

Thus, the value of the unknown resistance is $71.28\Omega$ .