A research sensor sends irregular bursts of current through a data cable. The current as a function of time during a single 12s transmission window is sampled at 1.0s intervals, producing the table below.
Time t (s): 0 1 2 3 4 5 6 7 8 9 10 11 12
Current I (A): 0.0 0.4 1.2 1.5 1.7 1.6 1.1 0.8 0.5 0.3 0.2 0.1 0.0
Use the information provided to respond to the tasks that follow. Show detailed reasoning, clearly state any assumptions, and maintain proper units.
(a) Using an appropriate numerical method, estimate the total charge that is transmitted during the 12s window. Explicitly state the method you choose and justify its suitability.
(b) Compute the average current during the intervals t=0–6s and t=6–12s. Comment on the operational difference between the first and second half of the window.
(c) Suppose the sensor’s memory can store a maximum of 9.0C per transmission window. Based on your result in part (a), evaluate whether the device risked exceeding its memory limit during this transmission, and support your answer quantitatively.
(d) Describe one practical way the sampling resolution or estimation procedure could be improved to yield a more accurate value for the transmitted charge. Explain the impact your proposed change would have on the calculated result.