Final answer:
To maintain a sensor output within 10% dynamic error, the time constant must be set appropriately. For an ECG monitor, it should be less than 100 microseconds, and the maximum capacitance calculated with a resistance of 1.00 kΩ would be 0.1 µF.
Step-by-step explanation:
To maintain a sensor output within 10% dynamic error of the input, the sensor's system needs to have an appropriate time constant. The time constant of a sensor system determines how quickly the system can respond to changes in the input. In electronic applications such as an ECG monitor, the RC (resistance-capacitance) time constant is crucial for ensuring that the monitor can detect changes in voltage over small time intervals.
For instance, an ECG monitor requires an RC time constant of less than 1.00 × 10² us (100 microseconds) to measure voltage variations effectively. If the resistance (R) of the circuit is given as 1.00 kΩ (1000 ohms), we can calculate the maximum capacitance (C) allowed using the formula τ = RC, where τ represents the time constant. Thus, the maximum capacitance would be τ/R = 100 µs / 1000 Ω = 0.1 µF.
In practice, limiting the capacitance to a value of less than 0.1 µF can be a challenge due to inherent stray capacitances and the availability of specific capacitance values. Components with precise capacitance values are necessary to meet the strict time constant requirements.