Formula of Ohm's Law: V = IR, Graph, Limits and Examples

The formula of Ohm's law is $V = IR$ : the potential difference across a conductor equals the current through it multiplied by its resistance. Put another way, at a fixed temperature the current in a metal wire is directly proportional to the voltage across it, and R is the constant of proportionality.

Rearranged, the law gives $I = V/R$ and $R = V/I$ , so any two of the three quantities fix the third. It is the first circuit law taught in Class 10 and the starting point for series and parallel networks in AP Physics 1 and Class 12. You will find its neighbours listed on the electricity formulas hub.

Quick facts

Formula
$V = IR$
Rearranged
$I = \frac{V}{R}$ , $R = \frac{V}{I}$
Units
volt (V), ampere (A), ohm (Ω)
Condition
Temperature and other physical conditions stay constant
Graph
V against I is a straight line through the origin, slope R
Local form
$J = \sigma E$

What the formula of Ohm's law says

Quantities in V = IR
Symbol	Quantity	SI unit	Measured with
$V$	Potential difference across the component	volt (V)	Voltmeter in parallel
$I$	Current through the component	ampere (A)	Ammeter in series
$R$	Resistance of the component	ohm (Ω)	Ratio V/I, or an ohmmeter

The law is a statement about a material, not a definition. The ratio V/I always gives a resistance, but Ohm's law claims more: for a metal at steady temperature that ratio stays the same as you change the voltage. A component passing 1 A under 1 V has a resistance of exactly 1 Ω, so 1 Ω = 1 V/A.

The V against I graph

Plot potential difference on the y axis against current on the x axis for a resistor kept cool. The points lie on a straight line through the origin. The slope of that line is the resistance. A steeper line means a larger resistance.

Many books plot I on the y axis instead. Then the slope is 1/R, called the conductance, measured in siemens (S). Check which axis is which before reading a slope from a graph question.

A curve, not a line, tells you the component is non ohmic. The ratio V/I at a point still gives its resistance at that current.

Ohm's law problems worked through

Problem 1: a torch bulb

A 12 V battery drives 0.50 A through a lamp. Find the lamp's resistance.

$R = \frac{V}{I} = \frac{12}{0.50} = 24\ \Omega$

Problem 2: a kettle on mains supply

A kettle element of resistance 26.5 Ω is connected to a 230 V supply. Find the current.

$I = \frac{V}{R} = \frac{230}{26.5} \approx 8.7\ \text{A}$

Problem 3: milliamps and kilohms

A current of 2.5 mA flows through a 4.7 kΩ resistor. Find the voltage across it.

Convert: I = 2.5 mA = 0.0025 A, R = 4.7 kΩ = 4700 Ω.

$V = IR = 0.0025 \times 4700 \approx 11.8\ \text{V}$

Milliamps times kilohms gives volts directly: 2.5 × 4.7 = 11.75, which is a handy shortcut.

Where the law holds and where it fails

Ohmic and non ohmic components
Component	Obeys Ohm's law?	Why
Metal wire at constant temperature	Yes	Resistance does not depend on current
Filament lamp	No	The filament heats up and its resistance rises
Semiconductor diode	No	Conducts easily one way, hardly at all the other way
Thermistor	No	Resistance falls as it warms
Electrolyte	Roughly, once current flows	Ions carry the charge

So the law has limits. It needs constant temperature, it fails for devices whose resistance depends on the direction of current, and it fails where V and I are not proportional at all. Inside a material, the same idea is written $J = \sigma E$ , linking current density to the electric field.

Linking V = IR to power and resistance

Combine Ohm's law with electrical power $P = VI$ and you get two more forms that save time:

$P = I^2 R \qquad P = \frac{V^2}{R}$

For the kettle in Problem 2, $P = V^2/R = 230^2/26.5 \approx 2.0 \times 10^3$ W, about 2 kW. The resistance R itself depends on the wire: $R = \rho L/A$ , from the resistivity formula and the resistance formula. For resistors in series, $R = R_1 + R_2 + \dots$ ; in parallel, $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$ . Apply V = IR to the whole circuit first, then to each resistor.

Mistakes that lose marks

Not converting mA and kΩ. Use amperes and ohms, or use the mA times kΩ shortcut consistently.
Applying the law to the wrong component. V must be the voltage across the same resistor that carries I.
Saying a lamp obeys Ohm's law. Its resistance changes as it heats.
Writing the law as V = R/I. Test it: a larger resistance with the same current must need a larger voltage.
Leaving out the condition. In a theory answer, always say physical conditions such as temperature stay the same.

Frequently asked questions

What is the formula of Ohm's law?

Ohm's law is V = IR, where V is potential difference in volts, I is current in amperes and R is resistance in ohms. It can also be written I = V / R or R = V / I.

Is the formula of ohms law different from V = IR?

No. Whether it is written with or without the apostrophe, the formula of ohms law is V = IR, with the two rearrangements I = V / R and R = V / I.

Which unit does R take in Ohm's law?

The ohm, symbol Ω. One ohm is the resistance through which 1 A flows when 1 V is applied, so 1 Ω = 1 V/A.

Why does a filament bulb not obey Ohm's law?

As the current rises, the filament gets hotter and its resistance increases. The V against I graph curves, so V and I are not proportional.

What is the slope of a V against I graph?

For an ohmic resistor the slope of V (y axis) against I (x axis) is the resistance R. If I is on the y axis, the slope is 1 / R.