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.