Instructions: Answer all questions.

What is a strain gauge? Explain the operation of Strain gauge.

A strain gauge is a sensor whose resistance varies with the amount of strain applied to the object to which it is attached. When the object is stretched or compressed, the gauge's material also stretches or compresses. This change in shape causes a change in the gauge's electrical resistance. Strain gauges are widely used in various applications, including load cells, pressure sensors, and accelerometers, to measure deformation.

Operation of a Strain Gauge:

The operation of a strain gauge is based on the principle of electrical resistance change due to mechanical deformation. When a conductor or semiconductor is subjected to mechanical strain (stretching or compression), its dimensions (length and cross-sectional area) change. This change in dimensions directly affects its electrical resistance.

Consider a conductor with an initial length L, cross-sectional area A, and resistivity ρ. Its initial resistance R is given by:

When strain (ε) is applied, the length changes by ΔL and the cross-sectional area changes by ΔA.

The new length becomes L' = L + ΔL and the new area becomes A' = A + ΔA.

The new resistance R' is:

For most metals, when stretched, their cross-sectional area decreases, and when compressed, their area increases. This phenomenon is related to Poisson's ratio (ν).

The change in resistance (ΔR) is related to the change in length (ΔL) and the change in area (ΔA).

The relationship between resistance, length, and area can be expressed in terms of strain. For small strains, the change in resistance is approximately proportional to the strain:

where Gf is the gauge factor, a material property that indicates the sensitivity of the strain gauge. For metallic strain gauges, the gauge factor is typically around 2. For semiconductor strain gauges, it can be much higher (up to 100-200).

The gauge factor is defined as:

The change in resistance is very small, so it is usually measured using a Wheatstone bridge circuit to amplify the output signal and compensate for temperature variations.

Instructions: Answer all questions.

Briefly define and explain all the static characteristics of transducers.

The static characteristics of a transducer describe its performance when the input is constant or changes very slowly. These characteristics are important for selecting a transducer for a specific application where the measured quantity does not change rapidly. The key static characteristics are:

1. Accuracy: This is the degree of closeness of measurements of a quantity to that quantity's actual (true) value. It is often expressed as a percentage of the full-scale reading or as a maximum error. For example, a transducer with an accuracy of ±1% FS means its readings can be off by up to 1% of the full-scale range.
2. Precision: This refers to the degree of reproducibility or repeatability of measurements under the same conditions. A precise transducer will give very similar readings for repeated measurements of the same input, even if those readings are not close to the true value (i.e., it can be precise but inaccurate).
3. Resolution: This is the smallest change in the input quantity that can be detected by the transducer and produce a corresponding change in the output. It is often expressed as a fraction of the full-scale range or as a specific value. For example, a digital thermometer with a resolution of 0.1°C can only display temperature changes in increments of 0.1°C.
4. Sensitivity: This is the ratio of the change in the output signal to the change in the input quantity. It indicates how much the output changes for a unit change in the input. A higher sensitivity means a smaller input change can produce a detectable output change. Mathematically, it is often represented as the slope of the input-output curve.
Sensitivity (S) = ΔOutput / ΔInput
5. Linearity: This describes how closely the actual input-output relationship of a transducer approximates a straight line. A perfectly linear transducer has a constant sensitivity across its entire operating range. Non-linearity is the deviation from this ideal straight line, often expressed as a percentage of the full-scale reading.
6. Hysteresis: This is the difference in output readings for the same input value when approached from different directions (e.g., increasing input vs. decreasing input). It is caused by factors like friction or magnetic effects within the transducer. The hysteresis error is typically expressed as the maximum difference in output over the operating range.
7. Threshold: This is the minimum value of the input quantity that is required to produce a detectable output signal. Below this threshold, the transducer may not respond at all, or its response may be erratic.
8. Dead Zone (or Dead Band): This is the range of input values over which the transducer does not respond or its response is negligible. It is closely related to threshold and hysteresis.
9. Range: This is the span of input values for which the transducer is designed to operate and provide meaningful measurements. It is usually specified as a minimum and maximum value (e.g., 0-100°C).
10. Span: This is the algebraic difference between the maximum and minimum values of the output signal. It represents the total output variation for the full input range.