EMF & Internal Resistance

Why real cells aren't perfect — and how to measure what's lost inside.

Spec Points Covered
  • I can define EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). and distinguish it from terminal p.d.
  • I can explain why cells have internal resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohms (Ω).The resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to current. Measured in ohms (Ω). within the source of EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). itself, which causes energyThe capacity to do work. Measured in joules (J). to be dissipated inside the source..
  • I can use the EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). equation in all its forms.
  • I can determine EMF and r from a V-I graph.
  • I can calculate total EMF and internal resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω).The resistance within the source of EMF itself, which causes energyThe capacity to do work. Measured in joules (J). to be dissipated inside the source. for cells in series and parallel.
  • I can design and evaluate an experiment to measure EMF and internal resistanceThe resistance within the source of EMF itself, which causes energyThe capacity to do work. Measured in joules (J). to be dissipated inside the source..
Notes
01 Electromotive force (EMF) Electromotive force (EMF) → 02 Internal resistance Internal resistance → 03 EMF equation (expanded form) → 04 Straight-line comparison → 05 Cells in series (same direction) → 06 Parallel cells: internal resistance → 07 Note 7 → 08 Note 8 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
EMF equation (expanded)
$$\varepsilon = IR + Ir$$
  • Where:
    • $\varepsilon$ = EMF of the source (V)
    • $I$ = current in the circuit (A)
    • $R$ = external resistance (ohm)
    • $r$ = internal resistance (ohm)
IR = terminal p.d. (useful), Ir = lost volts (wasted inside the cell). On the AQA data sheet as ε = I(R + r).
EMF definition
$$\varepsilon = \frac{E}{Q}$$
  • Where:
    • $\varepsilon$ = electromotive force (V)
    • $E$ = energy transferred by the source (J)
    • $Q$ = charge (C)
E is the total electrical energy the source gives to charge Q.
Terminal p.d.
$$V = \varepsilon - Ir$$
  • Where:
    • $V$ = terminal potential difference (V)
    • $\varepsilon$ = EMF (V)
    • $I$ = current (A)
    • $r$ = internal resistance (ohm)
V decreases as I increases. When I = 0, V = epsilon.
Lost volts
$$v = Ir$$
  • Where:
    • $v$ = lost volts (V)
    • $I$ = current (A)
    • $r$ = internal resistance (ohm)
Energy per coulomb wasted inside the cell.
Q Retrieval Practice All 10 Questions →
Q1. Define the electromotive forceThe energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). (EMF) of a powerThe rate of energy transfer. Measured in watts (W). supply and state its unit.
  • EMF is the electrical energy per unit charge produced by the source.
  • Unit: voltThe SI unit of potential difference and EMF. One volt is one joule per coulomb. (V).
Q2. What causes a cell to have internal resistance?
Collisions between charge carriers (electrons) and atoms inside the cell as current flows through it.
Q3. Write the EMF equation relating epsilon, I, R, and r.
epsilon = I(R + r), which expands to epsilon = IR + Ir.
Q4. What are 'lost voltsThe potential difference across the internal resistance of a cell. Equal to Ir.' and how are they calculated?
  • Lost voltsThe potential difference across the internal resistance of a cell. Equal to Ir. (v) are the p.d. dropped across the internal resistance.
  • Calculated as v = Ir.
Q5. How does terminal p.d. relate to EMF and lost voltsThe potential difference across the internal resistance of a cell. Equal to Ir.?
  • V = epsilon - Ir.
  • Terminal p.d. equals the EMF minus the lost volts.