PhysicsICSE Class 10 · Ohm's Law and Resistances

Ohm's Law: Statement, V–I Graph, Ohmic Conductors and Resistivity (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

Ohm's law states that the current through a conductor is directly proportional to the potential difference across its ends, provided its temperature and other physical conditions stay the same: V = IR. For an ohmic conductor the V–I graph is a straight line through the origin, and its slope gives the resistance R.

For an ohmic conductor, V against I is a straight line through the origin, and its slope ΔV/ΔI is the resistance R.

Illustration drawn for QuestionBuddy.

Understand Ohm's Law, V–I Graph and Resistivity

Charge, current and pd.

Charge $Q$ is measured in coulombs (C).
Current is the rate of flow of charge: $I = \frac{Q}{t}$ ; unit ampere, $1$ A $= 1$ C s⁻¹.
Potential difference between two points is the work done in moving unit charge from one to the other: $V = \frac{W}{Q}$ ; unit volt, $1$ V $= 1$ J C⁻¹.
Resistance is the opposition a conductor offers to current: $R = \frac{V}{I}$ ; unit ohm, $1$ Ω $= 1$ V A⁻¹.

Ohm's law. The current flowing through a conductor is directly proportional to the potential difference across its ends, provided the physical conditions (temperature, length, material and so on) remain unchanged:

$V \propto I \Rightarrow V = I R .$

The condition is part of the law: leave it out and the statement is incomplete.

Verifying Ohm's law. Connect a cell (battery), a plug key, a rheostat, an ammeter and the resistance wire in series, and a voltmeter in parallel across the wire. Close the key and note the ammeter and voltmeter readings. Change the rheostat to take several pairs of readings, keeping the current small so the wire does not heat up. For each pair, $\frac{V}{I}$ comes out the same, and a graph of $V$ against $I$ is a straight line passing through the origin. Its slope $\frac{Δ V}{Δ I}$ is the resistance $R$ . (If $I$ is plotted on the y-axis instead, the slope is $\frac{1}{R}$ .)

Ohmic and non-ohmic conductors.

Ohmic	Non-ohmic
Obey Ohm's law	Do not obey Ohm's law
V–I graph a straight line through the origin	V–I graph curved, or straight but not through the origin
$\frac{V}{I}$ constant for every reading	$\frac{V}{I}$ changes
Metal wires at constant temperature (copper, nichrome, manganin)	Filament lamp, junction diode, LED, electrolytes

To decide, check both that $\frac{V}{I}$ is the same for each reading and that the line would pass through the origin. A table where $V$ goes up in equal steps with $I$ but $\frac{V}{I}$ changes is non-ohmic.

Factors affecting the resistance of a wire.
1. Length: $R \propto l$ (a longer wire offers more opposition).
2. Area of cross-section: $R \propto \frac{1}{A}$ (a thicker wire offers less).
3. Material: through its resistivity.
4. Temperature: for metals, resistance increases with temperature. A wire that carries current for a long time heats up, so its resistance rises.

Combining the first three:

$R = ρ \frac{l}{A},$

where $ρ$ is the specific resistance (resistivity) of the material, unit Ω m. Resistivity depends only on the material and its temperature, not on the length or thickness (just as density depends only on the material). Copper has a low resistivity and is used for connecting wires; alloys such as nichrome have a high resistivity (and do not oxidise easily when hot), so they are used in heating elements.

Stretching a wire. If a wire is stretched to $n$ times its length, its volume stays the same, so its area becomes $\frac{1}{n}$ times; its resistance becomes $n^{2}$ times.

Superconductors. Certain materials lose all resistance when cooled below a particular very low temperature (the critical temperature). A current set up in a superconducting loop flows on without any loss. Uses: very strong electromagnets (MRI scanners, particle accelerators), magnetic levitation trains, and loss-free power cables under development.

Ohm's Law, V–I Graph and Resistivity: formulas and key facts

Ohm's law: $V = I R$; At constant temperature and other physical conditions.
Current and pd: $I = \frac{Q}{t}, V = \frac{W}{Q}$; 1 A = 1 C s⁻¹; 1 V = 1 J C⁻¹.
Resistance of a wire: $R = ρ \frac{l}{A}$; ρ in Ω m depends only on material and temperature.
Slope of the V–I graph: $R = \frac{Δ V}{Δ I}$; V on the y-axis, I on the x-axis.
Units: Charge coulomb (C)
Current ampere (A)
Potential difference volt (V)
Resistance ohm (Ω)
Resistivity ohm metre (Ω m); 1 Ω = 1 V A⁻¹.

Charge	coulomb (C)
Current	ampere (A)
Potential difference	volt (V)
Resistance	ohm (Ω)
Resistivity	ohm metre (Ω m)

How to solve Ohm's Law, V–I Graph and Resistivity questions

Decide which relation links the given quantities, convert units, and state conditions where the question asks for a law.

1For charge and energy data, use $I = \frac{Q}{t}$ and $V = \frac{W}{Q}$ (time in seconds), then $R = \frac{V}{I}$ .
2For a V–I table, compute $\frac{V}{I}$ for every reading and check whether the line passes through the origin before calling it ohmic.
3For a graph, take two well-separated points on the line: $R = \frac{Δ V}{Δ I}$ .
4For wire dimensions, use $R = ρ \frac{l}{A}$ with $l$ in m and $A$ in m² (1 mm² $= 1 0^{- 6}$ m²).
5For changes in a wire, use ratios: $R \propto l$ , $R \propto \frac{1}{A}$ , and stretching to $n$ times the length gives $n^{2}$ times the resistance.

Ohm's Law, V–I Graph and Resistivity in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Why a bulb's filament is non-ohmic

Suppose you measure a torch bulb's current at three voltages and find that doubling the voltage less than doubles the current.

Explain why the bulb does not obey Ohm's law.

Try it first, then show the solutionSolution

As the current increases, the filament gets much hotter.
A metal's resistance rises with temperature, so V/I grows; the physical condition (temperature) has not stayed the same.

Answer: The filament heats up, its resistance increases, so V is not proportional to I.

Memory hook: Hot wire, higher resistance.

Choosing wire for a heater and its leads

Imagine you are building an electric room heater. You need a heating coil and wires to connect it to the plug.

Which kind of material should each be made of, and why?

Try it first, then show the solutionSolution

Heating coil: a high-resistivity alloy such as nichrome, which produces much heat and does not oxidise easily when red hot.
Leads: low-resistivity copper, so very little energy is wasted in them and they stay cool.

Answer: Coil of nichrome (high ρ); leads of copper (low ρ).

Memory hook: Heat where you want it, not in the wires.

Tricks to remember Ohm's Law, V–I Graph and Resistivity

Short memory aids. Say each one aloud once, then use it on a question the same day.

VIR triangle
Cover the quantity you want: V = I × R, I = V ÷ R, R = V ÷ I.
Use it when: Rearranging Ohm's law.
Law plus condition
'Proportional, provided physical conditions stay the same': no condition, no full mark.
Use it when: Stating Ohm's law.
Two tests for ohmic
Straight AND through the origin; constant V/I for every reading.
Use it when: Data-table questions.
Resistivity is like density
Both depend only on the material (and temperature), never on size or shape.
Use it when: Resistance vs resistivity.

Ohm's Law, V–I Graph and Resistivity: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Doubling the pd · 1 mark · MCQBoard level

The pd across a metal wire is doubled while its temperature is kept constant. The current through it:
(a) halves
(b) stays the same
(c) doubles
(d) becomes four times

Try it first, then show the solutionSolution

By Ohm's law, $I \propto V$ at constant temperature, so the current doubles.

Answer: (c) doubles

Example 2: Stating and verifying Ohm's law · 4 marks · Long answerBoard level

(a) State Ohm's law. (b) Draw a labelled circuit diagram to verify it. (c) How is the resistance found from the graph?

Try it first, then show the solutionSolution

(a) The current through a conductor is directly proportional to the pd across its ends, provided its temperature and other physical conditions remain the same. (1)
(b) A cell, plug key, rheostat, ammeter and the resistance wire in series, with a voltmeter connected in parallel across the wire; conventional current from + to −. (2)
(c) Plot V (y-axis) against I (x-axis); the slope of the straight line through the origin is R. (1)

Answer: (a) I ∝ V at constant physical conditions (b) Series circuit with voltmeter across the wire (c) Slope of the V–I graph

Example 3: From charge and energy to resistance · 3 marks · Short answerHarder board level

In 2 minutes, 90 C of charge flows through a lamp, and 1080 J of electrical energy is converted. Find (a) the current, (b) the pd across the lamp, (c) its resistance.

Try it first, then show the solutionSolution

(a) $I = \frac{Q}{t} = \frac{90}{120} = 0.75$ A. (1)
(b) $V = \frac{W}{Q} = \frac{1080}{90} = 12$ V. (1)
(c) $R = \frac{V}{I} = \frac{12}{0.75} = 16$ Ω. (1)

Answer: (a) 0.75 A (b) 12 V (c) 16 Ω

Example 4: Is it ohmic? · 3 marks · Short answerHarder board level

Readings for a resistor: V = 1.5, 3.0, 4.5, 6.0 V; I = 0.25, 0.50, 0.75, 1.00 A. (a) Find V/I for each reading. (b) Is the resistor ohmic? Justify. (c) What is the slope of its V–I graph?

Try it first, then show the solutionSolution

(a) $\frac{1.5}{0.25} = \frac{3.0}{0.50} = \frac{4.5}{0.75} = \frac{6.0}{1.00} = 6$ Ω. (1)
(b) Yes: V/I is constant, and since V = 6I the line passes through the origin. (1)
(c) The slope is the resistance, 6 Ω. (1)

Answer: (a) 6 Ω each (b) Ohmic (c) 6 Ω

Example 5: A non-ohmic device · 3 marks · Short answerHarder board level

A device gives: V = 2, 4, 6 V; I = 0.40, 0.60, 0.75 A. (a) Calculate V/I for each. (b) Is the device ohmic? (c) Suggest what the device might be and why its V/I changes.

Try it first, then show the solutionSolution

(a) 5 Ω, about 6.67 Ω and 8 Ω. (1)
(b) No: V/I is not constant, so V is not proportional to I. (1)
(c) A filament lamp: as the current increases the filament gets hotter and its resistance rises. (1)

Answer: (a) 5, 6.67 and 8 Ω (b) Non-ohmic (c) A filament lamp heating up

Example 6: Resistance from dimensions · 2 marks · Short answerHarder board level

A resistance wire is 1.5 m long and has a cross-sectional area of 0.3 mm². The resistivity of its material is $1.0 \times 1 0^{- 6}$ Ω m. Find its resistance.

Try it first, then show the solutionSolution

$A = 0.3 \times 1 0^{- 6}$ m². (½)
$R = ρ \frac{l}{A} = \frac{1.0 \times 1 0 ^{- 6} \times 1.5}{0.3 \times 1 0 ^{- 6}} = 5$ Ω. (1½)

Answer: 5 Ω

Example 7: Case study: stretching and cutting · 4 marks · Case-basedHOTS / competency

A uniform wire has a resistance of 5 Ω.
(a) It is drawn out uniformly to twice its length. Find its new resistance.
(b) Does its resistivity change? Explain.
(c) The original wire is instead cut into two equal halves, which are joined in parallel. Find the resistance of the combination.
(d) The original and the stretched wire are each connected to a 2 V cell of negligible internal resistance. Find the current in each.

Try it first, then show the solutionSolution

(a) Length × 2, area × ½ (same volume), so $R \times 4 = 20$ Ω. (1)
(b) No: resistivity depends only on the material and temperature. (1)
(c) Each half is 2.5 Ω; in parallel, $\frac{2.5}{2} = 1.25$ Ω. (1)
(d) Original: $\frac{2}{5} = 0.4$ A; stretched: $\frac{2}{20} = 0.1$ A. (1)

Answer: (a) 20 Ω (b) No (c) 1.25 Ω (d) 0.4 A and 0.1 A

Where students lose marks in Ohm's Law, V–I Graph and Resistivity

The slips examiners see most often, and what to write instead.

Mistake: Incomplete statement of Ohm's law
The proportionality holds only if temperature and other physical conditions stay the same.
Wrong working
'V = IR' or 'I is inversely proportional to V'.
Right working
'The current through a conductor is directly proportional to the pd across it, provided the physical conditions remain unchanged.'
Do this: Learn the statement with its condition.
Usually costs: Reported by CISCE examiners for 2024 Q8(i)(c).
Mistake: Judging ohmic behaviour by slope alone
The V–I line must also pass through the origin, so that V/I is the same for every reading.
Wrong working
Readings with equal steps in V and I called ohmic without checking V/I.
Right working
Compute V/I for each reading; if it changes, the conductor is non-ohmic.
Do this: Do both checks and state both in the justification.
Usually costs: Reported by CISCE examiners for 2024 Q8(i).
Mistake: Treating resistivity like resistance
Resistivity depends only on the material and temperature, not on length or area.
Wrong working
'Specific resistance depends on the length of the wire.'
Right working
'Specific resistance depends on the material (and temperature) only.'
Do this: Compare it with density.
Usually costs: Reported by CISCE examiners for 2024 Q1(viii).
Mistake: Ignoring heating when current flows for a long time
Joule heating raises the temperature, so both resistance and resistivity increase.
Wrong working
'Resistivity stays the same as it is a constant.'
Right working
'Both resistance and resistivity increase as the wire heats up.'
Do this: Read 'long period of time' as a clue to heating.
Usually costs: Reported by CISCE examiners for 2025 Q3(vi).

Exam tips

In the verification circuit, the ammeter is in series and the voltmeter in parallel with the wire; mark + and − terminals.
Label the axes of a V–I graph with quantities and units, and draw the line through the origin.
Convert mm² to m² (× 10⁻⁶) before using $R = ρ \frac{l}{A}$ .
For a data table, justify 'ohmic' or 'non-ohmic' with calculated V/I values.

Practice questions on Ohm's Law, V–I Graph and Resistivity

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
One ohm is equal to:
(a) 1 V A
(b) 1 V A⁻¹
(c) 1 A V⁻¹
(d) 1 J C⁻¹
Hint
$R = \frac{V}{I}$ .
Answer
(b) 1 V A⁻¹
Q2 · 1 mark · Very short answerBoard level
A 40 Ω resistor is connected across 10 V. Find the current.
Hint
$I = \frac{V}{R}$ .
Answer
$I = \frac{10}{40} = 0.25$ A.
Q3 · 2 marks · Short answerHarder board level
The V–I graph of a wire is a straight line through the origin and the point (0.4 A, 10 V). Find the resistance of the wire.
Hint
Slope.
Answer
$R = \frac{10 - 0}{0.4 - 0} = 25$ Ω.
Q4 · 3 marks · Short answerBoard level
State how the resistance of a wire changes when (a) its length is increased, (b) its thickness is increased, (c) its temperature is increased.
Hint
$R = ρ \frac{l}{A}$ and the effect of heating.
Answer
(a) Increases ( $R \propto l$ ). (b) Decreases ( $R \propto \frac{1}{A}$ ). (c) Increases (for a metal).
Q5 · 2 marks · Short answerHarder board level
A wire of resistance 4 Ω is replaced by one of the same material with twice the length and half the cross-sectional area. Find the new resistance.
Hint
Both changes multiply R.
Answer
$R^{'} = 4 \times 2 \times 2 = 16$ Ω.
Q6 · 2 marks · Short answerHarder board level
What is a superconductor? Give one use.
Hint
Zero resistance below a temperature.
Answer
A material whose resistance becomes zero when it is cooled below a certain critical temperature. Use (any one): strong electromagnets in MRI scanners; maglev trains; loss-free transmission cables (being developed).
Q7 · 3 marks · Short answerHarder board level
A heater draws 4 A from a 230 V supply. (a) Find its resistance. (b) Assuming the resistance stays the same, find the current when the supply falls to 200 V. (c) Why might the actual current at 200 V differ slightly?
Hint
Temperature changes resistance.
Answer
(a) $R = \frac{230}{4} = 57.5$ Ω. (b) $I = \frac{200}{57.5} \approx 3.48$ A. (c) At a lower voltage the element is cooler, so its resistance is slightly lower and the current slightly higher than calculated.
Q8 · 2 marks · Short answerHOTS / competency
Wire A has length $l$ and area $A$ ; wire B, of the same material, has length $3 l$ and area $3 A$ . Find the ratio of their resistances and of their resistivities.
Hint
Ratio $\frac{l}{A}$ .
Answer
$R_{A} : R_{B} = \frac{l}{A} : \frac{3 l}{3 A} = 1 : 1$ . Resistivities are equal (1 : 1), being the same material.
Q9 · 3 marks · Short answerHOTS / competency
Wires X and Y are made of the same alloy. X is 1 m long with a cross-sectional area of 0.2 mm²; Y is 3 m long with an area of 0.5 mm². (a) Which has the greater resistance? Find the ratio $R_{X} : R_{Y}$ . (b) Each is connected in turn across the same cell of negligible internal resistance. Which carries the larger current, and in what ratio?
Hint
Compare $\frac{l}{A}$ ; current is inversely proportional to R.
Answer
(a) $R \propto \frac{l}{A}$ : for X, $\frac{1}{0.2} = 5$ ; for Y, $\frac{3}{0.5} = 6$ (same units). Y has the greater resistance and $R_{X} : R_{Y} = 5 : 6$ . (b) X carries the larger current; $I_{X} : I_{Y} = 6 : 5$ .

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Condition for Ohm's law?Show answer
Physical conditions such as temperature remain the same.
2.Slope of a V–I graph (V on y-axis)?Show answer
Resistance.
3.SI unit of resistivity?Show answer
Ω m.
4.A non-ohmic conductor?Show answer
Filament lamp (or diode).
5.Resistance when a wire is stretched to twice its length?Show answer
Four times.

Ohm's Law, V–I Graph and Resistivity: frequently asked questions

What is Ohm's law?

What is the difference between ohmic and non-ohmic conductors?

Ohmic conductors obey Ohm's law: their V–I graph is a straight line through the origin. Non-ohmic conductors, such as a filament lamp or a diode, do not: their V/I ratio changes.

On what factors does the resistance of a wire depend?

On its length (R ∝ l), its area of cross-section (R ∝ 1/A), its material (through its resistivity) and its temperature: R = ρl/A.