Fred, Bob and Linda have built an an electronic device. The gig runs in 3 minute cycles, it stays awake for 0.4s then sleeps for the remaining time in the cycle, that is 179.6s and then it starts again 420 times a day.
They measured that the gig draws 6mA in active mode and 4.3µA in sleep mode.
They are given a battery rated at 800mAh (that is considered to be "perfect" for this exercice)
They are being asked what will be the autonomy?
Fred's approach:
- You have 24h * 60 / 3min = 480 measurement cycles per day.
- Each measurement lasts 0.4s / 3600 = 0.00011 hours.
- so in awake mode the gig draws 6mA * 0.00011h * 480 = 0.3mAH per day.
- and in sleep mode (the rest of the time), it draws 0.0043mA * 23,947h = 0.1mAH per day.
Total = (0.3 + 0.1) = 0.4mAH.
so with an 800mAH battery: 800 / 0.4 = 2000h = ~66 days.
➜ Fred says 66 days.
Bob's approach:
- Per cycle:
- Consumption in awake mode = 6 mA × 0.4 s = 2.4 mA⋅s.
- Consumption in sleep mode = 0.0043 mA × 179.6 s= 0.77 mA⋅s.
- Total Consumption: 2.4 + 0.77 = 3.17 mA.s.
- Average consumption per second = 3.17mA.s / 180s = 0.0176mA.
- Average consumption per hour = 3600 x 0.0176mA = 63.4mA.h.
Battery autonomy = Battery capacity / Average consumption per hour.
➜ For an 800mA/h battery, we'll have 800 / 63.4= 12.61 hours.
Bob says ~12h30
Linda's approach:
800mAH theoretically means the battery can supply:
- 800mA for 1 hour,
- 400 mA for 2 hours,
- 200mA for 4 hours,
... - 6mA for 133 hours, which is 478,800 seconds.
You take 480 measurements of 0.4s each day, meaning you are awake for 480 x 0.4s = 192s in a day.
Neglecting standby consumption, we would have 478,800 / 192 = 2493 days, so probably a bit less when not neglecting standby.
Linda says ~ at least 5 years (the maths says 6.8 years).
So the results are :
Fred says 66 days.
Bob says ~12h30
Linda says ~ at least 5 years.
That's quite a difference...
QUESTION:
➜ Is one of them right and if so where is the reasoning mistake for the other 2 (or are the 3 wrong and you have another solution ?)
5 posts - 2 participants