# Relationship between power usage and time

Hello all,

I look forward to learning :)

EXPLANATION
There is a system with, lets say, 10 watt hours of energy available for use.
There is an inverse correlation between how much power we choose to use (energy use per second) and how quickly that systems energy will be completely drained.
The higher the power usage (the quicker we use energy) the lower the time is that it takes to fully drain that system.

For example
WATT/HOUR USED - TIME TILL 100% ENERGY USAGE
1 - 10 hours
5 - 8.75 hours
10 - 7.5 hours

Side note: Our system does replenish energy while work is being done, hence the "curve" on these above numbers.

QUESTIONS
1 - Have I explained the above correctly? I'm relatively new to physics terminology.
2 - Is there a term for the correlationship between power used, and how quickly the energy is drained to 100%? Low power usage = long time. High Power usage = short time. How do we measure or communicate this correlationship. For example colloquially how "intensity"... the power is
If there isn't a singular discrete term for this principal then is there another principal in physics that is similar, who's term could be high jacked?
i.e. a principal where 1 variable stays at 100% (energy usage), while 2 other variables have a coorelationship.(power usage vs time).
3 - The fact that the system replenishes even during work...is there a principle, term, or measurment for this?
4 - Is there a principal, term, or measurement if we only want to work until a certain % of energy is used...i.e. use 1 watt hour of power until 70% of the systems energy is sued.

Thanks again for your input, I look forward to learning.

Sean

mfb
Mentor
For example
WATT/HOUR USED - TIME TILL 100% ENERGY USAGE
1 - 10 hours
5 - 8.75 hours
10 - 7.5 hours
The first column is "Watt hours per hour", or simply Watt.

If nothing feeds the system, the values would be inversely proportional to each other, as power multiplied by time is energy:
1 W * 10h = 10 Wh
10 W * 1h = 10 Wh

If you have a constant flow of energy into the system, you have to know how much power goes in to figure out when your reserves are empty (or at 30%, or whatever).
i.e. a principal where 1 variable stays at 100% (energy usage), while 2 other variables have a coorelationship.(power usage vs time).
"A depends on B"?

Merlin3189
Homework Helper
Gold Member
There is a system with, lets say, 10 watt hours of energy available for use.
There is an inverse correlation between how much power we choose to use (energy use per second) and how quickly that systems energy will be completely drained.
The higher the power usage (the quicker we use energy) the lower the time is that it takes to fully drain that system.

For example
WATT/HOUR USED - TIME TILL 100% ENERGY USAGE
1 - 10 hours
5 - 8.75 hours
10 - 7.5 hours

Side note: Our system does replenish energy while work is being done, hence the "curve" on these above numbers.

QUESTIONS
1 - Have I explained the above correctly? I'm relatively new to physics terminology.
2 - Is there a term for the correlationship between power used, and how quickly the energy is drained to 100%? Low power usage = long time. High Power usage = short time. How do we measure or communicate this correlationship. For example colloquially how "intensity"... the power is
If there isn't a singular discrete term for this principal then is there another principal in physics that is similar, who's term could be high jacked?
i.e. a principal where 1 variable stays at 100% (energy usage), while 2 other variables have a coorelationship.(power usage vs time).
3 - The fact that the system replenishes even during work...is there a principle, term, or measurment for this?
4 - Is there a principal, term, or measurement if we only want to work until a certain % of energy is used...i.e. use 1 watt hour of power until 70% of the systems energy is sued.
I'm happy up to the start of the table of data. Then, Watt / hour is not usual. Since you say above that, energy per second, maybe you just mean Watt.

Then
Watt -----Time -------Energy Used ---Replenished Energy ---Replenishment Rate----Hidden Use --- New Replenishment Rate
1 ---------10 hr -------10 W hr --------------- 0 --------------------------------0----------------------7 W hr----------7 W
5 ---------8.75 hr --- 43.75 W hr -------- 33.75 W hr------------------ 6.75 W------------------6.125 W hr-----8 W
10 --------7.5 hr ------ 75 W hr--------- 65 W hr ----------------------- 6.5 W-------------------5.25 W hr------7 W
As you can see, apart from the first line, you are using more energy (Watt hours) than you have. So there must be replenishment. But there appears to be no replenishment in the first hour.
The other puzzling feature here is that your system (battery?) supplies more energy at a high discharge rate than at a low discharge rate. This is the reverse of what one would expect for a battery. It looks more like there is another hidden load. If there is a replenishment rate of 7 -8 W with a hidden load around one tenth of this, the sums come out a bit more evenly over the three sample points you list. (It's still not exact, so I'd like more data, or some explanation of the nature of your system.)
Hidden load could be some form of self discharge or a high internal resistance or inefficiency in a regulator or voltage converter. (More info beyond "system" might help decide this.)

Q2 - I'd say you were talking about energy measured in Joules or Watt hours (=3600 Joule) If you divide Energy in W hr by the load in W then you get the number of hours it will last. Obviously not what is shown here! But replenishment isn't a fixed energy source, rather a power source.
Also, depending on what your system is, some systems have an energy capacity which depends on the rate at which energy is drawn - eg. 10 W hr at 1 W, but only 9 W hr at 5 W and 8W hr at 10W, so that you only get near the full capacity at low loads.

Q3 - No idea what you call it. You need to know how this replenishment is occurring and consider this as a separate source.

Q4 - Again, I've no idea what the official term, if any, is for this. I might talk about usable capacity.

At the moment one can only treat the system as a black box. A white box might be easier to model.