Resistance and I–V Characteristics
Resistance measures how much a component opposes the flow of current. One equation does most of the work, and one set of graphs explains why some components obey it and others do not.
1. Ohm’s law
V = I R potential difference (V, volts) = current (I, amps) × resistance (R, ohms Ω)
Rearranged: I = V/R and R = V/I
Resistance is measured in OHMS (Ω), current in amps (A), potential difference in volts (V), and charge in coulombs (C). Forgetting the unit of charge was a recorded error; so was confusing “ampere” with the symbol for current in the formula.
Example: a 12 V supply drives 0.5 A through a resistor.
- R = V/I = 12 ÷ 0.5 = 24 Ω
Example: 6 V across an 18 Ω resistor.
- I = V/R = 6 ÷ 18 = 0.33 A
Divide, don’t multiply. A recorded error produced 72 A where 0.33 A was correct — multiplying 6 × 12 instead of dividing. Sanity-check: a bigger resistance must give a smaller current.
Convert milliamps to amps before calculating — 250 mA = 0.25 A. This was a specific recorded error and it shifts the answer by a factor of 1000.
Write the formula down before substituting. Tutors flagged this, and it earns method marks.
What the relationships mean
At constant resistance, current is directly proportional to voltage: double the voltage, double the current. At constant voltage, current is inversely proportional to resistance: double the resistance, halve the current.
“Inversely proportional” means one goes up as the other goes down, with their product constant. Uncertainty about this phrase was recorded — and the whole of Ohm’s law is built on it.
2. I–V characteristic graphs
These graphs plot current against potential difference. Their shape tells you whether a component obeys Ohm’s law.
The gradient is related to 1/R. A steeper line means a lower resistance. Where the graph curves, the resistance is changing.
Fixed resistor (metal wire at constant temperature)
- Straight line through the origin
- Current is directly proportional to voltage
- Resistance is constant — this is an ohmic conductor
Filament lamp
- S-shaped curve, flattening as voltage increases
- Resistance increases as the current increases
- Non-ohmic
Why it curves: a larger current heats the filament. The metal ions vibrate more, so electrons collide with them more often, and the resistance rises.
Resistance INCREASES with temperature for a metal. Saying it decreases was a recorded error. The exception is a thermistor, whose resistance decreases as it gets hotter.
Diode
- No current in the reverse direction (very high resistance)
- Current flows freely in the forward direction once a small threshold voltage is passed
- Non-ohmic — a diode allows current one way only
Connect components the right way round. Polarity matters for diodes, ammeters and voltmeters, and getting it wrong was flagged in lessons.
3. What resistance depends on
For a given wire at constant temperature:
Resistance is DIRECTLY proportional to LENGTH — a longer wire has more resistance. Resistance is INVERSELY proportional to CROSS-SECTIONAL AREA — a thicker wire has less resistance.
Why: in a longer wire, electrons travel further and collide with more ions. In a thicker wire, there are more paths for the electrons, so charge flows more easily.
So: doubling the length doubles the resistance; doubling the area halves it.
Scope note. Some lessons used the resistivity formula R = ρL/A. On 0625 these relationships are required qualitatively — you need to know that resistance goes up with length and down with area, and be able to compare two wires. The resistivity formula itself belongs to A-level. Check your own syllabus document before revising it.
Temperature: for a metal, higher temperature → more resistance. For a thermistor, higher temperature → less resistance.
4. Resistors in series and parallel
In series:
R_total = R₁ + R₂ + R₃ …
The total is always larger than the biggest individual resistor.
In parallel:
1/R_total = 1/R₁ + 1/R₂ + …
Example: 6 Ω and 3 Ω in parallel.
- 1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6
- R = 2 Ω
The total is always SMALLER than the smallest individual resistor. If your parallel answer is bigger than either resistor, you have forgotten to take the reciprocal at the end — the most common error, and one recorded repeatedly.
Adding resistors in parallel DECREASES total resistance, because you are adding more paths for the current.
For exactly two resistors in parallel, this shortcut is quicker:
R = (R₁ × R₂) / (R₁ + R₂) → (6 × 3)/(6 + 3) = 18/9 = 2 Ω ✓
5. Measuring resistance experimentally
Circuit: the component in series with an ammeter and a variable resistor, with a voltmeter in parallel across the component.
Ammeter in SERIES, voltmeter in PARALLEL. Always.
Method: vary the resistance to get several pairs of readings, plot I against V, and find R from the graph.
Take repeat readings and plot a graph rather than relying on one pair — this is the standard “improve the experiment” answer.
For a filament lamp, the resistance changes as it heats, so calculate R = V/I at each point rather than from a single overall gradient.
6. Mistakes that cost marks
Multiplying instead of dividing in V = IR.
Not converting mA to A.
Forgetting the reciprocal in the parallel formula.
Getting a parallel total bigger than the individual resistors.
Saying resistance decreases with temperature for a metal.
Confusing a thermistor’s behaviour with a metal’s.
Saying a filament lamp is ohmic.
Reading the gradient of an I–V graph as R rather than 1/R.
Connecting the ammeter in parallel or the voltmeter in series.
Omitting units.
Frequently asked questions
What is Ohm’s law? V = I R — potential difference equals current times resistance.
What is the unit of resistance? The ohm (Ω).
What is an ohmic conductor? One where current is directly proportional to voltage — a straight line through the origin on an I–V graph, at constant temperature.
Why does a filament lamp’s graph curve? As current rises the filament heats up, ions vibrate more, electrons collide more, and resistance increases.
What does a diode’s graph look like? Current flows in one direction only, after a small threshold voltage.
How does resistance depend on length and thickness? Directly proportional to length; inversely proportional to cross-sectional area.
What happens to a metal’s resistance as it heats up? It increases. A thermistor does the opposite.
How do I calculate resistors in parallel? 1/R = 1/R₁ + 1/R₂, then take the reciprocal.
Why is parallel resistance smaller? More paths are available for the current.
Where do the ammeter and voltmeter go? Ammeter in series, voltmeter in parallel.
Quick revision checklist
- I know V = IR and can rearrange it
- I know the units of V, I, R and charge
- I convert mA to A before calculating
- I understand direct and inverse proportionality here
- I can sketch the I–V graph for a resistor, filament lamp and diode
- I can explain why the lamp’s graph curves
- I know metals gain resistance when hot, thermistors lose it
- I know resistance rises with length and falls with area
- I know the resistivity formula is beyond 0625
- I can combine resistors in series
- I can combine resistors in parallel, remembering the reciprocal
- I can check a parallel answer is smaller than the smallest resistor
- I know where the ammeter and voltmeter go
- I write the formula before substituting, and give units
These notes cover resistance and I–V characteristics in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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