10.1 Electromotive Force

Batteries are the unsung heroes of our electronic world. They provide the juice that powers our devices, from smartphones to cars. Understanding how they work and their key characteristics is crucial for grasping the basics of electrical circuits.

Electromotive force (emf) and potential difference are key concepts in battery function. Chemical reactions inside batteries generate electrical energy, with different types of batteries using various materials. Calculating terminal voltage helps us understand how batteries perform under load.

Electromotive Force and Batteries

Emf and battery potential difference

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• Electromotive force (emf) represents the maximum potential difference between battery terminals when no current flows
  • Measured in volts (V)
  • Indicates the battery's capacity to drive current through a circuit
• Potential difference is the voltage drop across the battery when current flows
  • Always less than the emf due to internal resistance of the battery
• Relationship between emf ($\mathcal{E}$) and potential difference ($\Delta V$) given by $\Delta V = \mathcal{E} - Ir$
  • $I$ represents the current flowing through the battery
  • $r$ is the internal resistance of the battery
• The emf creates an electric field within the battery, driving the flow of charge

Chemical reactions in battery voltage

• Batteries generate electrical energy from chemical energy via redox reactions (oxidation-reduction reactions)
• Primary batteries are non-rechargeable and include:
  • Alkaline batteries (AA, AAA) with zinc (Zn) anode and manganese dioxide (MnO2) cathode
    • Zn oxidizes, releasing electrons while MnO2 reduces, accepting electrons
  • Lithium batteries (CR2032) with lithium (Li) anode and various cathode materials (manganese dioxide, carbon monofluoride)
    • Li oxidizes, releasing electrons and cathode material reduces, accepting electrons
• Secondary batteries are rechargeable and include:
  • Lead-acid batteries (car batteries) with lead (Pb) anode, lead dioxide (PbO2) cathode, and sulfuric acid (H2SO4) electrolyte
    • During discharge, Pb and PbO2 react with H2SO4 to form lead sulfate (PbSO4)
    • During charging, PbSO4 converts back to Pb and PbO2
  • Lithium-ion batteries (smartphone batteries) with graphite anode and lithium metal oxide cathode (LiCoO2, LiFePO4)
    • During discharge, Li ions move from anode to cathode while electrons flow through the external circuit
    • During charging, Li ions move back to the anode

Calculation of battery terminal voltage

• Terminal voltage ($V_T$) is the potential difference across battery terminals when current flows
• Relationship between terminal voltage, emf ($\mathcal{E}$), current ($I$), and internal resistance ($r$) given by $V_T = \mathcal{E} - Ir$
• To calculate terminal voltage:
  1. Identify the emf ($\mathcal{E}$) and internal resistance ($r$) of the battery
  2. Determine the current ($I$) flowing through the battery
  3. Substitute values into the equation $V_T = \mathcal{E} - Ir$
• Example: A 12 V battery has an internal resistance of 0.1 Ω and supplies a current of 5 A
  • Given: $\mathcal{E} = 12$ V, $r = 0.1$ Ω, $I = 5$ A
  • Calculation: $V_T = \mathcal{E} - Ir = 12$ V $- (5$ A$)(0.1$ Ω$) = 11.5$ V
  • The terminal voltage of the battery is 11.5 V when supplying a current of 5 A

Electrochemistry and Battery Function

• Electrochemistry is the study of chemical reactions that produce electrical energy
• Batteries convert chemical potential energy into electrical potential energy
• In a circuit, the battery's emf drives electron flow from the negative terminal to the positive terminal
• The electrochemical reactions in batteries involve the transfer of electrons between chemical species, creating a potential difference