Question

A strain gauge is used to measure weight of a substance based on the voltage generated by the strain gauge. In industry, strain gauges are calibrated by recording the voltage generated with respect to the load applied on the gauge. The following plot depicts experimental data of such calibrations.

How the applied weight and voltage of the gauge are correlated?
Also, find the approximate value of applied weight for a gauge output voltage of $1.2$ V.

• A. Positive correlation
• B. Negative correlation
• C. Approximate weight is $12$ kg.
• D. Approximate weight is $7$ kg.

Answer 1

Answer: (A), (D)

Approximate weight is $7$ kg.

From the figure, it is seen that with an increase in weight, the output voltage of the strain gauge increased.
Hence, it is a positive correlation.

Let's draw a line of best fit.

A trend line is a line around which all the given points are equally scattered. The trend line that captures the essence of the data is called the line of best fit.
To find the approximate applied weight for a given output voltage, follow the below steps:

1. Draw two horizontal lines above and below Voltage = 1.2 V.
2. These two lines will cut the line of best fit at two different points.
3. Drop two vertical lines from those points on the horizontal axis.
4. These vertical lines will cut the horizontal axis at around $6$ kg and $8$ kg.

From the given options, $7$ kg lies between $6$ kg and $8$ kg.
$\therefore$ The required answer is $7$ kg.

Hence, options (a) and (d) are correct.