Question

Express the equation for transducer bridge, if all the resistor values are equal

(a) v=-(△R×Vdc)/(2×R+△R)

(b) v=-(△R×Vdc)/2×(R+△R)

(c) v=-Vdc/[2×(2×R+△R)].

(d) v=-(△R×Vdc)/ [2×(2×R+△R)].

This question was addressed to me in quiz.

Query is from Instrumentation Amplifier topic in section Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

The correct answer is:

(d) v=−ΔR×Vdc2×(2R+ΔR)v = -\frac{\Delta R \times V_{\text{dc}}}{2 \times (2R + \Delta R)}v=−2×(2R+ΔR)ΔR×Vdc​​

Explanation:

A transducer bridge typically uses resistors in a Wheatstone bridge configuration to measure changes in resistance ($\Delta R$) caused by a physical parameter such as pressure, temperature, or strain. The output voltage $v$ is derived based on the following assumptions:

1. All resistors initially have the same resistance $R$, and one or more resistors change by a small amount $\Delta R$.
2. VdcV_{\text{dc}}Vdc​ is the supply voltage applied to the bridge.

The general equation for the output voltage $v$ of a transducer bridge, taking into account a small change in resistance, is given as:

v=−ΔR×Vdc2×(2R+ΔR)v = -\frac{\Delta R \times V_{\text{dc}}}{2 \times (2R + \Delta R)}v=−2×(2R+ΔR)ΔR×Vdc​​

This equation accurately reflects the relationship between the resistance change ($\Delta R$), the DC supply voltage (VdcV_{\text{dc}}Vdc​), and the output voltage $v$.