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19.2Electric Current and Circuits

Resistance and Ohm’s Law — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 4 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

Define resistance and use R = V/I.Resistance = potential difference ÷ currentR = V/I (Ω = V/A).RearrangedV = IR and I = V/R.For a wireR = ρL/A — resistance ∝ length and ∝ 1/cross-sectional area (Supplement: proportionality).Cross-sectional area of a round wireA = πd2/4 = πr2.Powe…

  • Thermistor
  • A resistor has a p.d. of 9.0 V across it and a current of 0.30 A. Find its resistance
  • Ohmic conductor
  • Non-ohmic component
  • Variable resistor (rheostat)
  • Filament lamp

Section 1 of 7Resistance and Ohm’s Law

1
19.2 Resistance and Ohm's Law concept map: Resistance = potential differ, Rearranged, For a wire, Cross-sectional area of a rou, Thermistor
Visual guide to the key ideas explained in this lesson.
2
Resistance measures how much a component opposes current. For a given p.d., a larger resistance means a smaller current.
3
To measure resistance, record the p.d. across the component with a voltmeter in parallel and the current through it with an ammeter in series, then calculate R = V/I.
4
In a metal, electrons collide with vibrating positive ions in the lattice. These collisions transfer energy to the ions (heating the wire) and are the cause of resistance.
5
At constant temperature a metal wire obeys Ohm's law: doubling V doubles I, so the I–V graph is a straight line through the origin and R is constant.
6
In a filament lamp, a larger current heats the filament; the ions vibrate more, collisions increase and resistance rises. So the I–V graph curves towards the V-axis (gradient decreases).
7
A diode has very high resistance in reverse and low resistance in the forward direction once a small threshold p.d. is exceeded. It can be used to convert a.c. to d.c. (rectification).
8
The resistance of a wire is directly proportional to its length: charges must travel through twice as many collisions in a wire twice as long.
9
The resistance of a wire is inversely proportional to its cross-sectional area: a thicker wire gives more paths for the charge, like a wider pipe.
10
An NTC thermistor's resistance decreases as temperature rises; it is used in thermostats and fire alarms. An LDR's resistance decreases as light intensity increases; it is used in automatic street lights.
11
Combining P = IV with V = IR gives P = I2R, which shows why transmission cables lose a lot of power as heat when the current is large.
12
When an I–V graph is plotted with I on the y-axis, a steeper line means a smaller resistance.
13
Use a low p.d. and switch off between readings so the component does not heat up during a resistance experiment.

Section 2 of 7Process & sequence

1
Connect a cell/power supply, a variable resistor, an ammeter and the component under test in series.
2
Connect a voltmeter in parallel across the component.
3
Set the variable resistor to give a small current; record V and I.
4
Adjust the variable resistor to obtain at least 6 pairs of readings over the range.
5
Reverse the supply connections and repeat to obtain negative values (important for a diode).
6
Plot a graph of current (y-axis) against p.d. (x-axis).
7
Calculate R = V/I at several points; switch off between readings to avoid heating.

Why a filament lamp's resistance increaseswrite these steps in this order; each step is a marking point.

1
The p.d. across the lamp is increased, so the current increases.
2
More energy is transferred to the filament each second, so its temperature rises.
3
Metal ions in the filament vibrate with larger amplitude.
4
Free electrons collide more often with the ions.
5
The resistance increases, so current rises less than proportionally: the I–V graph curves.

Section 3 of 7Compare

I–V characteristics of common components
ComponentShape of I–V graphHow resistance behavesReason
Fixed resistor (constant T)Straight line through originConstantObeys Ohm's law
Filament lampCurve that flattens at higher VIncreases as V (and I) increaseFilament gets hotter; ions vibrate more and impede electrons
DiodeNear zero current in reverse; current rises sharply above about 0.6 V forwardVery high in reverse, low in forwardAllows current in one direction only
ThermistorCurve bending upwardsDecreases as temperature risesMore free charge carriers when hotter
LDR—Decreases as light intensity risesLight releases more charge carriers
How wire dimensions affect resistance
Change to wireEffect on R
Double the lengthR doubles (R ∝ L)
Double the cross-sectional areaR halves (R ∝ 1/A)
Double the diameterArea ×4, so R becomes one quarter
Heat a metal wireR increases

Resistance of a wireR = ρL/A, where ρ is resistivity (Ω m).

Section 4 of 7Worked examples

30 Ω

A resistor has a p.d. of 9.0 V across it and a current of 0.30 A. Find its resistance.

  • R = V/I = 9.0 V ÷ 0.30 A = 30 Ω.
5.0 Ω
A wire of length 1.2 m has resistance 4.0 Ω. What is the resistance of a 3.0 m length of the same wire with double the cross-sectional area?
  • R ∝ L
    • 4.0 × (3.0/1.2) = 10 Ω.
    • R ∝ 1/A: 10 ÷ 2 = 5.0 Ω.
12 V
A 240 Ω resistor carries a current of 0.050 A. Find the p.d. across it and the power transferred.
  • V = IR = 0.050 × 240 = 12 V.
    • P = I2R = 0.0502 × 240 = 0.60 W .
      What the symbols mean: V = potential difference (V) · I = current (A) · R = resistance (Ω)
      • (check: IV = 0.050 × 12 = 0.60 W)

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Resistance · Ohm (Ω) · Ohm's law · Ohmic conductor · Non-ohmic component · Resistor · Variable resistor (rheostat) · Filament lamp · Diode · Light-dependent resistor (LDR) · Thermistor (NTC) · Resistivity · Conductor / insulator
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
resistance is how hard it is for current to flowresistance is the p.d. across a component divided by the current through it (R = V/I).
2
Ohm's law is V = IRcurrent is directly proportional to p.d. for a metallic conductor at constant temperature.
3
a thicker wire has more resistanceresistance is inversely proportional to cross-sectional area, so a thicker wire has less resistance.
4
a thermistor's resistance goes up with heatthe resistance of an (NTC) thermistor decreases as temperature increases.
5
the lamp's resistance increases because current increasesthe filament's temperature rises, ions vibrate more, so resistance increases.

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