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Understanding EMF and Battery Resistance

Sep 1, 2025

Overview

This lecture explains electromotive force (EMF) in batteries, distinguishes between ideal and non-ideal batteries, and shows how to determine EMF graphically using a voltage-current (VI) curve.

Ideal vs. Non-Ideal Batteries

  • EMF (electromotive force) is the ideal potential difference a battery should provide, symbolized by ε (epsilon) and measured in volts.
  • In an ideal battery, there is no internal resistance, so the terminal voltage equals the EMF.
  • Terminal voltage is the actual measured voltage across a battery’s terminals.
  • For ideal batteries, terminal voltage (V) = EMF = current (I) × external resistance (R), so V = IR.
  • Real batteries have internal resistance (r), which reduces terminal voltage: V = EMF − I·r.
  • Internal resistance is an inherent property of the battery and always appears in series with external resistance.

Using Loop Rule and Equations

  • Applying the loop rule: sum of voltages around a circuit loop is zero.
  • In a non-ideal battery: EMF = I(R + r), as internal and external resistances add in series.
  • Increasing current increases voltage drop across internal resistance, decreasing terminal voltage.

Key Takeaways on Terminal Voltage

  • Terminal voltage in a real battery is V = EMF − I·r; as current increases, terminal voltage decreases.
  • If there is no current, terminal voltage equals EMF (no drop from internal resistance).
  • Maximum terminal voltage is only achieved at zero current.

Graphical Representation (VI Curve)

  • Plotting terminal voltage (V) vs. current (I) yields a straight line with negative slope.
  • The slope of the VI curve is negative internal resistance (−r).
  • The y-intercept of the graph is the EMF, representing the voltage when no current flows.

Key Terms & Definitions

  • EMF (Electromotive Force) — The ideal voltage a battery can provide, symbolized by ε, measured in volts.
  • Terminal Voltage — The actual voltage measured across the battery’s terminals.
  • Internal Resistance (r) — The inherent resistance inside a battery that reduces terminal voltage.
  • VI Curve — A graph of terminal voltage vs. current, used to determine EMF and internal resistance.

Action Items / Next Steps

  • Review EMF, terminal voltage, and internal resistance concepts.
  • Practice analyzing VI curves to find EMF and internal resistance.
  • Prepare for problems applying the loop rule to circuits with real batteries.