Batteries

Batteries are electrochemical cells whose voltage are determined by chemistry, $V_{\text{cell}}$, not size (AAA vs. D). There are rechargeable and non-rechargeable ones.

• Non-Rechargeable (“Primary”):
  • Typical alkaline battery
  • $V_{\text{cell}}=1.5\text{ V}$
• Rechargeable (“Secondary”):
  • Lithium-Ion (LiIon), Lithium Polymer (LiPo), Nickle Metal Hydride (NiMH), Nickle Cadmium (NiCd)
  • Widely varying $V_{\text{cell}}$

A very basic model of a battery is to consider it as a voltage source. However, this is a vast oversimplification as there are lots of factors like internal resistance, aging, etc.

Battery Summary

• Batteries have very complex behaviour
• $V_{cell}$ is chemistry dependent (SoC curve too)
• $C_{\text{cell}}$ increases with physical size, proxy for $Q_{\text{cell}}$
• $E_{\text{cell}}=Q_{\text{cell}}\cdot V_{\text{cell}}$
• $V_{total}=N\cdot V_{\text{cell}}$ (series)
• $C_{total}=M\cdot C_{\text{cell}}$ (parallel)
• $E_{total}=Q_{total}\cdot V_{total}=M\cdot N\cdot Q_{\text{cell}}\cdot V_{\text{cell}}$
  • E has units of joules ($J$) or watt-hours ($A\cdot h\cdot V=w\cdot h$)
• State of charge: SoC, like an indicator: 0 = Empty, 1 = full
  • ”Discharge curve” – plot of V vs SoC, depends on chemistry
  • Recharge: $I_r=P\cdot C_{\text{total}}$, values depends on chemistry

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