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Ohm's Law Explained: Formula, Derivation, Graph & Limitations

A complete Class 10 & Class 12 Physics guide to Ohm's Law — statement, formula (V=IR), derivation (microscopic and vector form), V-I graph, the Ohm's law triangle, power formula, series/parallel circuits, applications, and limitations.

Physics 23 September, 2026 17 min read

Last updated: September 23, 2026

What is Ohm's Law?

Ohm's Law Definition & Statement

Ohm's law states that the current flowing through a conductor between two points is directly proportional to the voltage (potential difference) across those two points, provided the temperature and other physical conditions remain constant. It was formulated by German physicist Georg Simon Ohm in 1827.

In simple terms (Ohm's law kya hai? in Hindi — "what is Ohm's law"), it tells us that if you double the voltage across a conductor, the current through it also doubles, as long as the resistance and temperature stay the same.

Key Terms: Voltage, Current & Resistance

Voltage Definition (Potential Difference)

Voltage, also called potential difference, is the electrical "pressure" that pushes electric charge through a circuit. It is defined as the work done per unit charge in moving a charge between two points. The SI unit of voltage is the volt (V).

Current Definition

Electric current is the rate of flow of electric charge through a conductor. It is defined as the amount of charge flowing per unit time: I = Q/t. The SI unit of current is the ampere (A).

Resistance Definition

Resistance is the opposition offered by a conductor to the flow of electric current. It depends on the material, length, cross-sectional area, and temperature of the conductor. The SI unit of resistance is the ohm (Ω).

Resistivity & Conductors

Resistivity (ρ) is an intrinsic property of a material that quantifies how strongly it resists current flow, independent of its shape or size. Resistance and resistivity are related by: R = ρL/A, where L is length and A is cross-sectional area. A good conductor (like copper or silver) has low resistivity, while an insulator has very high resistivity.

Voltage, Current & Resistance in a Circuit V R (Resistance) A Current (I) V pushes current I through resistance R — V = IR Ammeter (in series) measures current; a voltmeter (in parallel) measures voltage

Figure 1: A simple circuit showing voltage (battery), resistance (resistor), and current measured by an ammeter.

Ohm's Law Formula & Triangle

Ohm's Law Formula

V = I × R

Where V = voltage (volts), I = current (amperes), R = resistance (ohms). Rearranged: I = V/R and R = V/I.

The Ohm's Law Triangle

The Ohm's law triangle is a simple memory aid for quickly recalling all three rearrangements of the formula.

Ohm's Law Triangle V I R Cover V → see I × R  |  Cover I → see V/R  |  Cover R → see V/I

Figure 2: The Ohm's law triangle — cover the quantity you want to find, and the remaining two show you the formula.

Ohm's Law Wheel (V, I, R, P Chart)

An extended version called the Ohm's law wheel (or Ohm's law chart) combines Ohm's law with the power formula, giving 12 different ways to calculate voltage, current, resistance, or power depending on which two quantities are known.

To FindGiven I and RGiven V and IGiven V and RGiven P and I
Voltage (V)V = IR——V = P/I
Current (I)——I = V/RI = √(P/R)
Resistance (R)—R = V/I—R = V²/P
Power (P)P = I²RP = VIP = V²/R—

Interactive Ohm's Law Simulation (V = IR Calculator)

Drag the voltage and resistance sliders below and watch the current respond instantly. The battery gains cells as voltage rises, the resistor fills with more atoms (obstacles) as resistance rises, the flowing charges speed up or slow down, and the letters in V = I × R grow or shrink with their values — a hands-on way to see Ohm's law at work.

Your browser does not support the canvas element, so the interactive Ohm's law simulation cannot be shown.
Voltage6.0 V
Current (I = V / R)12.0 mA
Resistance500 Ω

Moving dots show charge flow in the direction of conventional current (the arrows). Gray dots inside the resistor are atoms that obstruct the flow — more atoms means higher resistance.

Things to Try

  1. Keep R fixed and double V — the current doubles too (V ∝ I, the heart of Ohm's law).
  2. Keep V fixed and double R — the current is cut in half (I ∝ 1/R).
  3. Set V = 0 and notice that no current flows — no voltage, no push on the charges.
  4. Watch how the sizes of V, I and R in the equation change as you move each slider.

Derivation of Ohm's Law

The deduction of Ohm's law can be approached in two ways: the macroscopic (circuit-level) form and the microscopic (electron-level) form.

Microscopic Form of Ohm's Law

Deriving from Drift Velocity

When an electric field E is applied across a conductor, free electrons experience a force and acquire a drift velocity vd proportional to E: vd = (eEτ)/m, where e is electron charge, τ is relaxation time, and m is electron mass.

The current density is J = nevd, where n is the number density of free electrons. Substituting vd:

J = σE

This is the microscopic form of Ohm's law, where σ (sigma) = ne²τ/m is the conductivity of the material.

Vector Form of Ohm's Law

Vector Form

J⃗ = σE⃗

Since current density (J) and electric field (E) are both vector quantities pointing in the same direction (for an isotropic conductor), Ohm's law can be written in vector form as J⃗ = σE⃗, showing that current density flows in the direction of the applied electric field.

Multiplying the microscopic form by the conductor's length (L) and cross-sectional area (A) and simplifying gives us back the familiar macroscopic form: V = IR.

Ohm's Law Graph (V-I Characteristic)

The Ohm's law graph, also called the V-I characteristic curve, is obtained by plotting voltage (V) on the y-axis against current (I) on the x-axis for an ohmic conductor.

Ohm's Law V-I Graph (Ohmic Conductor) I (A) V (V) Slope = R (Resistance) 0

Figure 3: The V-I graph for an ohmic conductor is a straight line passing through the origin. The slope of this line gives the resistance (R = V/I).

For a device that obeys Ohm's law (an ohmic device), this graph is always a straight line through the origin, confirming that V is directly proportional to I. Devices that don't produce a straight-line graph (like diodes) are called non-ohmic.

Verifying Ohm's Law Experimentally (Class 10)

The classic Class 10 Ohm's law experiment verifies the V ∝ I relationship using a simple circuit. Here's how it works conceptually:

Circuit Setup

  • A resistor (the conductor under test) is connected to a battery through a rheostat (to vary the current).
  • An ammeter is connected in series with the resistor to measure the current (I) flowing through it.
  • A voltmeter is connected in parallel across the resistor to measure the voltage (V) across it.
  • A key/switch completes the circuit.

Procedure (conceptual): By adjusting the rheostat, several different values of current are set up, and the corresponding voltmeter and ammeter readings are recorded. When V is plotted against I, a straight line passing through the origin is obtained — confirming Ohm's law. The slope of this line gives the resistance of the conductor.

Try It Yourself: PhET Ohm's Law Simulation

If you want to explore this relationship interactively without physical equipment, the free PhET Ohm's Law simulation (from the University of Colorado Boulder) lets you adjust voltage and resistance sliders and watch the current respond in real time — a great way to build intuition for V = IR.

Ohm's Law in Series & Parallel Circuits

Ohm's Law in a Series Circuit

In a series circuit, the same current flows through all components, but voltage divides across each resistor. Total resistance: Rtotal = R₁ + R₂ + R₃ + ...

Ohm's Law in a Parallel Circuit

In a parallel circuit, the voltage across each branch is the same, but current divides among the branches. Total resistance: 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ...

PropertySeries CircuitParallel Circuit
CurrentSame through all componentsDivides among branches
VoltageDivides across componentsSame across all branches
Total ResistanceSum of individual resistancesReciprocal sum (always less than smallest R)

Power Formula & Ohm's Law

Electrical Power Formula

P = V × I

Combining this with Ohm's law (V = IR) gives two more useful forms:

P = I²R   and   P = V²/R

These three equivalent forms of the power formula let you calculate electrical power using whichever two quantities (V, I, or R) you already know.

Applications of Ohm's Law

  • Circuit design — calculating the correct resistor values needed for a desired current or voltage.
  • Fuse rating — determining safe current limits for electrical wiring and appliances.
  • Voltage dividers — designing circuits that split voltage into specific proportions.
  • Troubleshooting — diagnosing faults in circuits by measuring V, I, and R and checking against expected values.
  • Heating elements — calculating power dissipation in resistive heating devices like electric heaters and toasters.

Limitations of Ohm's Law

Two Key Limitations of Ohm's Law

  1. Does not apply to non-ohmic devices: Devices like diodes, transistors, and vacuum tubes do not have a constant resistance — their V-I graph is not a straight line, so Ohm's law does not hold for them.
  2. Requires constant physical conditions: Ohm's law only holds when temperature and other physical conditions (like pressure and strain) remain constant. If a conductor heats up significantly as current flows, its resistance changes, and the V-I relationship deviates from linearity.

Additionally, Ohm's law does not apply to unilateral devices (components like diodes that behave differently depending on the direction of current flow), and it does not apply to devices that show a change in the relationship between V and I at different values of applied voltage.

Solved Examples

Example 1: Finding Current

Question: A resistor of 10 Ω is connected across a 20V battery. Find the current flowing through it.

Solution:

Given: V = 20V, R = 10 Ω

I = V/R = 20/10 = 2 A

Example 2: Finding Resistance

Question: A current of 0.5 A flows through a conductor when a voltage of 12V is applied. Find its resistance.

Solution:

Given: V = 12V, I = 0.5 A

R = V/I = 12/0.5 = 24 Ω

Example 3: Power Dissipated

Question: Find the power dissipated in a 5 Ω resistor carrying a current of 3 A.

Solution:

Given: R = 5 Ω, I = 3 A

P = I²R = 3² × 5 = 9 × 5 = 45 W

Class 10 vs Class 12: How the Syllabus Differs

AspectClass 10Class 12
FocusBasic statement, formula, and experimental verificationMicroscopic/vector form, drift velocity derivation
CircuitsSimple series and parallel combinationsComplex networks, Kirchhoff's laws, Wheatstone bridge
Mathematical depthAlgebraic (V=IR)Vector calculus (J = σE)

Quick Revision Summary

Ohm's LawV = IR (at constant temperature)
Microscopic FormJ = σE
Power FormulaP = VI = I²R = V²/R
LimitationsFails for non-ohmic devices (diodes) and varying temperature

Frequently Asked Questions (FAQ)

Ohm's law states that current through a conductor is directly proportional to the voltage across it, provided temperature and other physical conditions remain constant. It is expressed as V = IR.

The formula is V = IR, where V is voltage, I is current, and R is resistance. It can be rearranged as I = V/R or R = V/I.

Voltage (potential difference) is the electrical pressure pushing charge through a circuit, measured in volts. Current is the rate of flow of charge, measured in amperes. Resistance is the opposition to current flow, measured in ohms.

Ohm's law can be derived from drift velocity of electrons under an electric field, giving the microscopic form J = σE. Scaling this by a conductor's dimensions gives the macroscopic form V = IR.

The Ohm's law triangle is a memory aid with V at the top and I, R at the bottom. Covering the unknown quantity reveals the formula to calculate it — cover V for I×R, cover I for V/R, cover R for V/I.

Ohm's law does not apply to non-ohmic devices like diodes and transistors, and it only holds when temperature and other physical conditions remain constant during current flow.

Combining P = VI with Ohm's law gives P = I²R and P = V²/R, letting you calculate power from any two of the three quantities V, I, and R.

Connect a resistor with an ammeter in series and voltmeter in parallel, vary the current using a rheostat, and plot V against I. A straight line through the origin confirms Ohm's law, with the slope giving the resistance.

Related Topics in Physics

Wheatstone Bridge Diodes Electric Current Resistivity Series & Parallel Circuits Kirchhoff's Laws Electrical Power Class 10 Physics Class 12 Physics