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Theme B — The Particulate Nature of Matter

B.5.11 Electromotive Force and Internal Resistance — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 52 of 53 1 quiz

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Lesson summary

B.5.11 Electromotive Force and Internal Resistance — IB PHYSICS SL notes: Define e.m.f., apply ε = I(R + r) and the terminal p.d. V = ε − Ir, and find ε and r experimentally.What the symbols mean: E or ε = e.m.f.

  • E.m.f. (ε)
  • Meaning of a value
  • Contrast with p.d
  • Open circuit
  • Internal resistance (r)
  • Lost volts

Part 1 of 7Electromotive force

E.m.f. (ε)
  • E.m.f. (ε) the energy transferred to each unit charge as it passes through the source
  • ε = W / q, measured in volts.
  • It is the amount of chemical energy converted to electrical energy per coulomb.
Meaning of a value
  • Meaning of a value an e.m.f. of 1.5 V means 1.5 J of chemical energy is transferred to each coulomb passing through the cell
Name
  • Name the term is historical, since e.m.f. is an energy per charge and not a force
Contrast with p.d.
  • Contrast with p.d. the p.d. across a component is the energy transferred from each coulomb to that component
Open circuit
  • Open circuit e.m.f. equals the p.d. across the cell when no current flows
  • It is measured by a high-resistance voltmeter connected across the terminals of the cell.

Part 2 of 7Internal resistance

Internal resistance (r)
  • Internal resistance (r) the resistance between the terminals of a power supply, caused by the materials inside it
  • A real source is modelled as an ideal e.m.f. with a small resistor r in series.
Effect
  • Effect some electrical energy is dissipated inside the source, so the cell warms up
Lost volts
  • Lost volts the term Ir is the p.d. lost across the internal resistance
Property
  • Property r belongs to the cell and does not change when external components change

Part 3 of 7Equations for a real source

E.m.f. equation
  • ε = I(R + r) = IR + Ir
  • R is the external (load) resistance and I is the current.
  • The e.m.f. is the total, or maximum, voltage available to the circuit.
Terminal p.d.
  • V = IR = ε − Ir
    What the symbols mean: V = potential difference (V) · I = current (A) · R = resistance (Ω)
  • It is the p.d. across the load.
Check
  • Check the lost volts plus the terminal p.d. must equal the e.m.f.
Total resistance
  • Total resistance always include r when finding the current, I = ε/(R + r)

Part 4 of 7Behaviour of a real source

Falling load resistance
  • Falling load resistance the current rises, more e.m.f. is lost internally and the terminal p.d. falls
Short circuit
  • Short circuit when R ≈ 0 the current reaches its maximum, I = ε/r
  • All the power is dissipated inside the cell, which can overheat.
Low internal resistance
  • Low internal resistance a car lead–acid battery (about 0.01 Ω) delivers large currents with little voltage drop
High internal resistance
  • High internal resistance a small cell cannot supply large currents
Ageing
  • Ageing internal resistance rises as a cell runs down
  • An old battery can show a normal e.m.f. on a voltmeter yet fail to light a bulb.

Part 5 of 7Power and efficiency

Total power
  • Total power the source supplies εI
Power in the load
  • I2R = VI
Power wasted inside
  • I2r
Efficiency
  • VI/εI = V/ε = R/(R + r)
Maximum power transfer
  • Maximum power transfer the power in the load is largest when R = r
  • Only half the power is then delivered, so the efficiency is 50%.
  • Sources for large loads aim for a low r instead.

Part 6 of 7Cells in combination

Cells in combination
Cells in series
  • Cells in series their e.m.f.s add and their internal resistances add
Identical cells in parallel
  • Identical cells in parallel the e.m.f. stays the same but the internal resistance divides by the number of cells
  • The combination can supply larger currents for longer.
Link
  • Link the resistor-combination rules of B.5.8 apply to the internal resistances

Part 7 of 7More from the specification

More from the specification
Electromotive Force and Terminal Potential Difference
  • Electromotive force (emf, epsilon) is the total energy transferred per unit charge into electrical form by a source,
  • whereas terminal potential difference V is the available voltage across external components: V = epsilon - Ir.
Terminal Voltage versus Current Characteristics
  • Graphing terminal potential difference V against current I yields a straight line with a negative gradient equal to -r and a positive y-axis intercept equal to the emf epsilon.
    • (internal resistance)
Internal Resistance and Lost Volts
  • As current output increases, the potential difference dropped across the internal resistance of the cell increases,
    • (lost volts = Ir)
  • reducing external terminal potential difference.
Resistivity and Thermistor Characteristics
  • In a negative temperature coefficient (NTC) thermistor,
  • increasing temperature releases additional charge carriers, decreasing material resistivity and reducing electrical resistance.
Resistivity
  • Property of a material defined by ρ = RA/L.
Thermistor
  • Resistor whose resistance falls as temperature rises.
Temperature
  • Measure of the average kinetic energy of the particles.
Conductor
  • Material that allows current to flow.
Circuit diagram
  • Drawing of a circuit using standard symbols.
Light intensity
  • How bright the light falling on a surface is.
Fixed resistor
  • Resistor with a resistance that cannot change.
Conventional current
  • Current drawn from the positive to the negative terminal.

Key terms

TermMeaning
E.m.f.Energy transferred to each coulomb passing through the source, ε = W/q.
Internal resistanceResistance of the source itself, r.
Terminal p.d.p.d. across the source terminals when current flows, V = ε − Ir.
Lost voltsIr, energy per coulomb dissipated inside the source.
Short circuitConnection of negligible resistance across the source; the current is ε/r.
Maximum power transferOccurs when the load resistance equals the internal resistance.

Avoid these mistakes

1
Saying the terminal p.d. always equals the e.m.f. — it does only when no current flows.
2
Putting the voltmeter across the load and calling its reading the e.m.f.
3
Reading r as the positive gradient of the V–I graph — the gradient is negative and r is its magnitude.
4
Forgetting to include r in the total resistance when finding the current.
5
Describing e.m.f. as a force measured in newtons.

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