Answer :
The pressure reading if the transmitter is sending a 4 psi signal can be calculated using linear interpolation within the given scaling range of 100 to 300 psi. The correct answer is option (c) 116.67 psi.
To explain, linear interpolation involves finding a proportional value within a known range based on a given value. In this case, the scaling is from 100 to 300 psi, which spans a range of 200 psi. The corresponding value for a 4 psi signal can be calculated using the formula:
\[
\text{Pressure Reading} = \text{Minimum Value} + \left( \frac{\text{Given Signal} - \text{Minimum Signal}}{\text{Maximum Signal} - \text{Minimum Signal}} \right) \times (\text{Maximum Value} - \text{Minimum Value})
\]
Substituting the values, we get:
\[
\text{Pressure Reading} = 100 + \left( \frac{4 - 100}{300 - 100} \right) \times (300 - 100) = 116.67 \, \text{psi}
\]
This calculation illustrates that when the transmitter sends a 4 psi signal, the corresponding pressure reading is approximately 116.67 psi, which matches option (c). Linear interpolation is commonly used to estimate values within a known range based on given data points.
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