In a certain commercial Wheatstone bridge, R1 is a fixed 1-kΩ resistor, R3 can be adjusted in 1-Ω steps from 0 to 1100 Ω, and R2 can be selected to be 1 kΩ, 10 kΩ, 100 kΩ, or 1 MΩ. a. Suppose that the bridge is balanced with R3 = 732 Ω and R2 = 10 kΩ. What is the value of Rx? b. What is the largest

Question

In a certain commercial Wheatstone bridge, [latex]R_1[/latex] is a fixed 1-kΩ resistor, [latex]R_3[/latex] can be adjusted in 1-Ω steps from 0 to 1100 Ω, and [latex]R_2[/latex] can be selected to be 1 kΩ, 10 kΩ, 100 kΩ, or 1 MΩ. a. Suppose that the bridge is balanced with [latex]R_3[/latex] = 732 Ω and [latex]R_2[/latex] = 10 kΩ. What is the value of [latex]R_x[/latex]? b. What is the largest value of [latex]R_x[/latex] for which the bridge can be balanced? c. Suppose that [latex]R_2[/latex] = 1 MΩ. What is the increment between values of [latex]R_x[/latex] for which the bridge can be precisely balanced?

Accepted Answer

1. From Equation 2.91, we have

[latex]R_x = \frac{R_2}{R_1}R_3[/latex] (2.91)

[latex]R_x = \frac{R_2}{R_1}R_3=\frac{10 kΩ}{1 kΩ}[/latex] × 732 Ω = 7320 Ω

Notice that [latex]R_2/R_1[/latex] is a scale factor that can be set at 1, 10, 100, or 1000, depending on the value selected for [latex]R_2[/latex]. The unknown resistance is the scale factor times the value of [latex]R_3[/latex] needed to balance the bridge.
2. The maximum resistance for which the bridge can be balanced is determined by the largest values available for [latex]R_2[/latex] and [latex]R_3[/latex]. Thus,

[latex]R_{x max} = \frac{R_{2 max}}{R_1}R_{3 max}=\frac{1 MΩ}{1 kΩ}[/latex] × 1100 Ω = 1.1 MΩ

3. The increment between values of [latex]R_x[/latex] for which the bridge can be precisely balanced is the scale factor times the increment in [latex]R_3[/latex]:

[latex]R_{xinc} = \frac{R_2}{R_1}R_{3inc}=\frac{1 MΩ}{1 kΩ}[/latex] × 1 Ω = 1 kΩ

Question 2.23: In a certain commercial Wheatstone bridge, R1 is a fixed 1-k...

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