{{tag>conversions battery chapter1_1}}
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#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~  Conversions: Battery                   #@TaskText_HTML@#   

1. How many minutes could an ideal battery with $10~{\rm kWh}$ operate a consumer with $3~{\rm W}$?

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\begin{align*}
W &= 10~{\rm kWh} &&= 10'000~{\rm Wh}\\ \\
t &= {{W             }\over{P        }} 
 &&= {{10'000~{\rm Wh}}\over{3~{\rm W}}} \\
&&&= 3'333~{\rm h}= 200'000~{\rm min} \quad (= 139~{\rm days})
\end{align*}
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\begin{align*}
t = 200'000~{\rm min}
\end{align*}
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2. Hard: Why is a real Lithium-ion battery with $10~{\rm kWh}$ not able to provide the given power for the calculated time?

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There are additional losses:
  * The battery has an internal resistance. Depending on the current provided by the battery, this leads to internal losses. 
  * The internal resistance of the battery is depending on the state of charge (SoC) of the battery.
  * The wires also add additional losses to the system.
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