Ohm's Law and V = IR

This lesson covers Ohm's law and the equation $V = IR$V=IR, as required by the Edexcel GCSE Combined Science specification (1SC0). You will learn what Ohm's law states, how to use and rearrange the equation, and the difference between ohmic and non-ohmic conductors.

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The Equation V = IR

The relationship between potential difference, current and resistance is:

$V = IR$V=IR

where:

• V = potential difference in volts (V)
• I = current in amperes (A)
• R = resistance in ohms ($\Omega$Ω)

This equation applies to any component in a circuit — it is the definition of resistance.

Rearranging

You will frequently need to rearrange this equation:

To find...	Rearranged form
Voltage (V)	$V = IR$V=IR
Current (I)	$I = \frac{V}{R}$I=RV​
Resistance (R)	$R = \frac{V}{I}$R=IV​

Exam Tip: Use a formula triangle to help you rearrange. Place V at the top, I at the bottom left and R at the bottom right. Cover the quantity you want to find — the remaining two show you the calculation.

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What Is Ohm's Law?

Ohm's law states:

The current through a conductor is directly proportional to the potential difference across it, provided the temperature remains constant.

This means:

• If you double the voltage, the current doubles (at constant temperature).
• A graph of V against I is a straight line through the origin.
• The gradient of this line equals the resistance.

Important Distinction

• $V = IR$V=IR is always true — it is a definition of resistance.
• Ohm's law is an additional statement about proportionality that only applies to certain conductors (called ohmic conductors) at constant temperature.

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Ohmic Conductors

An ohmic conductor is a component where the current is directly proportional to the voltage at constant temperature. The I-V graph is a straight line through the origin.

Examples of Ohmic Conductors
A wire at constant temperature
A fixed resistor (at constant temperature)

For an ohmic conductor, the resistance is constant — it does not change as the current or voltage changes.

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Non-Ohmic Conductors

A non-ohmic conductor does not obey Ohm's law — its resistance changes as conditions change.

Component	Behaviour
Filament lamp	Resistance increases as the filament heats up
Diode	Very high resistance in one direction; low resistance in the other
Thermistor	Resistance changes with temperature
LDR	Resistance changes with light intensity

These components have curved I-V graphs (filament lamp) or strongly asymmetric graphs (diode).

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Worked Examples

Worked Example 1

A 12 V battery is connected to a 4 $\Omega$Ω resistor. Calculate the current.

$I = \frac{V}{R} = \frac{12}{4} = 3 \text{ A}$I=RV​=412​=3 A

Worked Example 2

A current of 2.5 A flows through a heater connected to a 230 V supply. Calculate the resistance.

$R = \frac{V}{I} = \frac{230}{2.5} = 92 \; \Omega$R=IV​=2.5230​=92Ω

Worked Example 3

A current of 0.5 A flows through a 20 $\Omega$Ω resistor. Calculate the potential difference across it.

$V = IR = 0.5 \times 20 = 10 \text{ V}$V=IR=0.5×20=10 V

Exam Tip: Always show your working clearly: write the equation, substitute the values, and give the final answer with the correct unit. Even if you make an arithmetic error, you can still gain marks for method.

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Combining V = IR with Series and Parallel Rules

Example: Series Circuit

A 9 V battery is connected in series with a 3 $\Omega$Ω resistor and a 6 $\Omega$Ω resistor.

Step 1 — Total resistance:

$R_{\text{total}} = 3 + 6 = 9 \; \Omega$Rtotal​=3+6=9Ω

Step 2 — Current:

$I = \frac{V}{R_{\text{total}}} = \frac{9}{9} = 1 \text{ A}$I=Rtotal​V​=99​=1 A

Step 3 — Voltage across each resistor:

$V_1 = 1 \times 3 = 3 \text{ V}$V1​=1×3=3 V

$V_2 = 1 \times 6 = 6 \text{ V}$V2​=1×6=6 V

Check: $3 + 6 = 9 \text{ V}$3+6=9 V (correct).

Example: Parallel Circuit

A 12 V battery is connected to two resistors in parallel: 4 $\Omega$Ω and 6 $\Omega$Ω.

Current through each branch:

$I_1 = \frac{12}{4} = 3 \text{ A}$I1​=412​=3 A

$I_2 = \frac{12}{6} = 2 \text{ A}$I2​=612​=2 A

$I_{\text{total}} = 3 + 2 = 5 \text{ A}$Itotal​=3+2=5 A

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Temperature and Resistance

For metallic conductors:

• As temperature increases, the metal ions vibrate more.
• Moving electrons collide with the ions more frequently.
• This increases the resistance.

This is why a filament lamp does not obey Ohm's law — the filament gets very hot, so its resistance changes as the current increases.

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Summary

• $V = IR$V=IR links potential difference, current and resistance and applies to all components.
• Ohm's law states that current is directly proportional to voltage at constant temperature — this only applies to ohmic conductors.
• An ohmic conductor has a constant resistance and a straight-line I-V graph through the origin.
• Non-ohmic components (filament lamp, diode, thermistor, LDR) have a changing resistance.
• Always show your working: write the equation, substitute values, include units.
• For metals, resistance increases with temperature because ions vibrate more.

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Extended Worked Examples

Worked Example 4 — Checking Whether a Component Is Ohmic

A student records the following readings from a component. Is it an ohmic conductor?

V / V	I / A
1.0	0.05
2.0	0.10
3.0	0.15
4.0	0.20

Compute $R = V/I$R=V/I at each point:

V / V	I / A	R / $\Omega$Ω
1.0	0.05	20
2.0	0.10	20
3.0	0.15	20
4.0	0.20	20

Resistance is constant, so the component is an ohmic conductor. The I-V graph would be a straight line through the origin with gradient $1/R = 0.05 \text{ A/V}$1/R=0.05 A/V.

Worked Example 5 — Non-ohmic Data

A filament lamp gives the following readings.