Ohm's law

Every circuit you have ever wired — a torch, a doorbell, a school ammeter-voltmeter setup — obeys one quiet rule: push more potential difference across a conductor and, at constant temperature, the current grows in exact step with it. That rule is Ohm's law, the centrepiece of the CBSE Class 10 chapter "Electricity," and it is what lets you predict current from voltage, voltage from resistance, or resistance from a pair of meter readings without ever opening the circuit again. Ohm's law builds directly on the two ideas that come just before it in the chapter — current $I = Q/t$ , the rate of flow of charge, and potential difference $V = W/Q$ , the work done per unit charge in moving it around the circuit. Once those are in place, Ohm's law is what turns a circuit diagram into a set of numbers you can actually calculate: given any two of $V$ , $I$ , and $R$ , you can always find the third. This article compresses that one idea into everything you need for boards: the precise statement of the law, the $V = IR$ family of equations and the unit ohm, the experimental circuit that verifies it and the straight-line V–I graph it produces, a worked numerical, and the traps that cost the most marks.

The core insight

At constant temperature, current through a conductor is directly proportional to the potential difference across it, $V = IR$ , where the constant $R$ is the conductor's resistance in ohms.

The core idea

Ohm's law states that, at constant temperature, the current $I$ through a conductor is directly proportional to the potential difference $V$ applied across its two ends, provided the physical conditions of the conductor (especially temperature) do not change.

V \propto I \quad \Rightarrow \quad V = IR

where: $V$ is the potential difference in volts, $I$ is the current in amperes, and $R$ is the constant of proportionality for that conductor, called its resistance. The law is a statement about one specific conductor at one fixed temperature — change the conductor, or let it heat up, and $R$ itself can change. Rearranging gives the three equivalent forms every student should be able to use interchangeably:

V = IR, \qquad I = \dfrac{V}{R}, \qquad R = \dfrac{V}{I}

Resistance is the property of a conductor that opposes the flow of current through it, converting some electrical energy into heat — this is why wires and appliances warm up in use. Physically, resistance comes from collisions between the flowing electrons and the fixed atoms of the conductor: the more often electrons are scattered on their way through, the harder it is to push current, and the larger $R$ turns out to be. Its SI unit is the ohm, symbol $\Omega$ (the capital Greek letter omega):

1\ \Omega = \dfrac{1\ \text{V}}{1\ \text{A}}

A conductor has a resistance of 1 ohm if a potential difference of 1 volt across it drives a current of exactly 1 ampere through it.

Verifying it experimentally. A circuit is built with a resistor, an ammeter in series, a voltmeter in parallel across the resistor, a rheostat, a battery, and a plug key. The ammeter must always be connected in series so the full circuit current passes through it, and the voltmeter must always be connected in parallel across just the resistor, so it measures the potential difference across that component alone — mixing these up is a common wiring mistake in the practical. The rheostat's only job is to change the current in controlled steps so several $(V, I)$ pairs can be recorded, typically five or six readings across a safe range so the current does not overheat the wire. Plotting $V$ on the y-axis against $I$ on the x-axis gives a straight line through the origin — direct proof that $V \propto I$ — and the slope of that line equals $R$ . A conductor obeying this straight-line law is called ohmic (metals at constant temperature); one that does not (such as a diode or a heated filament) is non-ohmic, though non-ohmic behaviour is not examined quantitatively at this level, only recognised from the shape of its graph.

Figure

A V-I graph showing a straight line through the origin with V on the vertical axis and I on the horizontal axis, the slope of the line labelled as the resistance R

Derivation

Derivation AGetting resistance from a straight-line V-I graph

The goal is to show, using nothing beyond the definition of a straight line through the origin, why the slope of the experimental V–I graph gives the resistance R of the conductor — the single fact that connects the raw meter readings a student records in the lab to the number $R$ they must report, and that also explains why $V/I$ stays the same at every point on that line even though V and I individually change from reading to reading.

Step 1. Start from Ohm's law itself. For a given conductor at constant temperature, $V = IR$ with $R$ a fixed number. This is exactly the equation of a straight line $y = mx$ if we set $y = V$ , $x = I$ , and $m = R$ — a line with zero intercept, since $V = 0$ whenever $I = 0$ .

Step 2. Take any two readings from the experiment, say $(I_1, V_1)$ and $(I_2, V_2)$ , both taken on the same conductor at the same temperature. Then $V_1 = I_1 R$ and $V_2 = I_2 R$ , because $R$ has not changed between readings.

Step 3. Divide the two equations. $\dfrac{V_2 - V_1}{I_2 - I_1} = \dfrac{I_2 R - I_1 R}{I_2 - I_1} = \dfrac{R(I_2 - I_1)}{I_2 - I_1} = R$ . The left-hand side is precisely the rise-over-run definition of slope on a $V$ versus $I$ graph, so the slope computed from any two points on the line equals $R$ .

Step 4. Read the result. Because this holds for every pair of points, all the plotted $(I, V)$ readings must lie on one straight line through the origin, and that line's slope is the conductor's resistance — this is exactly why the experimental graph is used to extract $R$ rather than trusting a single meter reading, which could carry error.

Worked example

A resistor of resistance 5 Ω is connected across a battery of potential difference 10 V.

Step 1. Write down what is given: $R = 5\ \Omega$ , $V = 10\ \text{V}$ , and the quantity to find is the current $I$ .

Step 2. Choose the rearranged form of Ohm's law that isolates $I$ : $I = \dfrac{V}{R}$ .

Step 3. Substitute and compute: $I = \dfrac{10\ \text{V}}{5\ \Omega} = 2\ \text{A}$ .

Answer: a current of 2 A flows through the resistor.

Competitive stretch

Suppose the same resistor is later tested at two different settings of a rheostat: a current of 0.4 A is measured when $V = 2\ \text{V}$ . Step 1. Find $R$ from this reading: $R = V/I = 2/0.4 = 5\ \Omega$ , matching the resistor's known value, confirming $R$ has stayed constant. Step 2. Predict the current if $V$ is raised to 5 V at the same temperature: $I = V/R = 5/5 = 1\ \text{A}$ . Step 3. Check consistency: $V/I = 5/1 = 5\ \Omega$ again — the same ratio at every reading, which is exactly what makes the V–I graph a single straight line with slope $R = 5\ \Omega$ .

Common traps

Forgetting the constant-temperature condition — Ohm's law strictly applies only when the conductor's physical state, especially temperature, does not change during the measurement.
Swapping the axes of the V–I graph — by convention V goes on the y-axis and I on the x-axis, so the slope gives R directly, not 1/R.
Mixing units when substituting into $V = IR$ — current left in mA instead of converted to A is the most common numerical slip.
Assuming every conductor is ohmic — only conductors like metal wires at constant temperature give a straight line through the origin; a diode does not.

Ask the tutor: Stuck on a V–I graph question or a resistance numerical — ask the AI tutor for a fresh worked example or a step-by-step walkthrough of your own problem.

Why does the V-I graph have to pass through the origin?

Because Ohm's law says $V = IR$ with $R$ fixed, and when there is no current there is no potential difference driving it — $I = 0$ forces $V = 0$ . So the point (0, 0) is always on the line for an ideal ohmic conductor. If a real experimental line misses the origin slightly, that usually points to a measurement offset in the meters rather than to a failure of Ohm's law itself, and CBSE numericals always assume the ideal case passing through the origin.

What is the actual role of the rheostat in the Ohms law experiment?

The rheostat is a variable resistor whose job is only to change the current flowing in the circuit, step by step, so that several different pairs of V and I readings can be recorded from the ammeter and voltmeter. It does not itself get measured or plotted — it simply lets you collect enough points to draw a reliable straight line and read off its slope as R. Without it you would have only a single fixed reading, which is not enough to confirm a straight-line relationship.

Does Ohms law apply to every device, like a diode or a bulb filament?

No. Ohm's law only holds for ohmic conductors, mainly metals at constant temperature, which is why a resistance wire in the school lab gives a clean straight line. A bulb filament heats up as current increases, so its resistance itself changes and its V–I graph curves rather than staying straight. A diode conducts well in one direction and barely at all in the other, so it is strongly non-ohmic. CBSE Class 10 only expects you to identify ohmic versus non-ohmic behaviour qualitatively from the shape of the graph, not to calculate with the non-ohmic case.