Answer:
The non-linearity error is approximately 3.34, or 334% of the full range. This means that the resistance of the potentiometer deviates from the expected linear relationship by 334% of the full range.
Step-by-step explanation:
The non-linearity error of a potentiometer is a measure of how closely the resistance of the potentiometer follows a linear relationship as the wiper moves along the resistive element. In other words, it tells you how closely the resistance of the potentiometer follows a straight line as the wiper is moved.
To calculate the non-linearity error of a potentiometer, you need to know the resistance of the potentiometer and the load resistance, as well as the position of the wiper. In this case, the potentiometer has a resistance of 1kΩ and a load resistance of 10kΩ, and the wiper is at one-third of its maximum displacement.
The non-linearity error can be calculated using the following formula:
Non-linearity error = (measured resistance - expected resistance) / full range
Where "measured resistance" is the resistance of the potentiometer at the wiper's current position, "expected resistance" is the resistance that would be expected if the potentiometer were perfectly linear, and "full range" is the total resistance range of the potentiometer (i.e. the difference between the maximum and minimum resistance values).
To calculate the non-linearity error in this case, we first need to determine the expected resistance at the wiper's current position. Since the wiper is at one-third of its maximum displacement, we can assume that the resistance is also one-third of the maximum resistance of the potentiometer. Therefore, the expected resistance is 1kΩ * (1/3) = 333.3Ω.
Next, we need to determine the measured resistance at the wiper's current position. The total resistance of the circuit is equal to the resistance of the potentiometer in series with the load resistance. Since the potentiometer and the load are in series, their resistances add up. Therefore, the total resistance is 1kΩ + 10kΩ = 11kΩ. Since the wiper is at one-third of its maximum displacement, we can assume that the resistance at this position is one-third of the total resistance. Therefore, the measured resistance is 11kΩ * (1/3) = 3.67kΩ.
Finally, we can use the formula to calculate the non-linearity error:
Non-linearity error = (3.67kΩ - 333.3Ω) / (1kΩ - 0Ω)
Non-linearity error = 3.34kΩ / 1kΩ
Non-linearity error = 3.34
Therefore, the non-linearity error is approximately 3.34, or 334% of the full range. This means that the resistance of the potentiometer deviates from the expected linear relationship by 334% of the full range.