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Math Help - Can't see the solution to this simple question regarding Battery Capacity

  1. #1
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    Can't see the solution to this simple question regarding Battery Capacity

    Hi guys.

    I have a simple question but I just can't see the solution. Maybe I don't have enough information to be able to answer it?
    It seems simple enough!

    A sensor transmits at a duty cycle of 8%
    It uses a current of 2.5mA when it is active and 0 when it's not active
    On average it transmits 500 b of data per transmission. Each transmission lasts roughly 0.5ms

    If the battery capacity is 3000mAh then how long a transmission can the battery support before it runs out of juice?

    Those are the only numbers we're given in the question. The wording is slightly different if I can remember correctly but it's asking ''how long a transmission'' can the battery take?
    It seems very unclear to me.

    What do you guys think? How would I go about solving this?
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  2. #2
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    Re: Can't see the solution to this simple question regarding Battery Capacity

    Could you remind what a duty cycle is?

    Quote Originally Posted by mathtastic View Post
    Each transmission lasts roughly 0.5ms.

    If the battery capacity is 3000mAh then how long a transmission can the battery support before it runs out of juice?
    Is the word "transmission" used in two different senses? The problem statement says that a transmission lasts 0.5ms.
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  3. #3
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    Re: Can't see the solution to this simple question regarding Battery Capacity

    I think it uses transmission in the same context.
    I thought it's asking how long would the battery last if it were to receive one long continuous transmission? But i don't think there's enough information in the question to answer that.

    A duty cycle is the % of time it's being used. i.e. a duty cycle of 8% means the sensor is active 8% of the time, and 92% of the time it's in sleep or inactive
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  4. #4
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    Re: Can't see the solution to this simple question regarding Battery Capacity

    If the sensor transmits continuously, then the battery will obviously last for (3000 / 2.5) hours. In this case, most information in the problem statement is unnecessary. If the sensor works at a duty cycle of 8%, then the word "transmission" in "how long a transmission can the battery support" is used in a different sense from "transmission" in "Each transmission lasts roughly 0.5ms". The latter refers to continuous transmission, while the former refers to bursts of transmissions in the latter sense. In this case (when the sensor works intermittently), the battery will last for (3000 / 2.5) / 0.08 hours.
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