Potential difference, resistance and Ohm's law
IB Physics SLΒ· Topic 2: Electricity and MagnetismΒ· 12 min read
1. Defining Potential Differenceβ β ββββ± 10 min
Potential difference (pd) describes the amount of energy transferred per unit charge as charge carriers move between two points in a circuit. It is measured with a voltmeter connected in parallel across the two points, as this setup ensures the voltmeter draws negligible current and samples the full energy difference between the points.
Calculate the potential difference across a filament bulb that transfers 600 J of light and heat energy to 200 C of charge passing through it.
- 1
Start with the formal definition of potential difference
- 2
- 3
Substitute the given values E = 600 J, Q = 200 C
- 4
- 5
Final answer: potential difference across the bulb is 3 V
2. Electrical Resistanceβ β ββββ± 10 min
Resistance quantifies how much a circuit component opposes the flow of electric current. For a fixed applied potential difference, higher resistance results in lower current flowing through the component. Resistance in metallic conductors arises from collisions between moving free electrons and the vibrating positive ions of the metal lattice.
Resistance
The ratio of the potential difference across a component to the current flowing through it at a specific operating point
Example:
A 10 Ξ© fixed resistor allows 0.1 A of current when 1 V is applied across its terminals
A current of 0.4 A flows through a fixed resistor when 12 V is applied across it. Calculate the resistance of the resistor.
- 1
Rearrange the resistance definition formula to isolate R
- 2
- 3
Substitute the measured values V = 12 V, I = 0.4 A
- 4
- 5
Final answer: resistance of the resistor is 30 Ξ©
3. Ohm's Lawβ β β βββ± 12 min
Ohm's law is an empirical relationship that applies to most metallic conductors at constant temperature. It states that the current flowing through a conductor is directly proportional to the potential difference applied across it, as long as all physical conditions including temperature and pressure remain unchanged.
Derive the standard mathematical form of Ohm's law
Observed proportionality between current I and potential difference V for constant temperature
- 1
Write the proportionality relationship: I β V
- 2
Introduce a constant of proportionality equal to 1/R, where R is fixed resistance
- 3
- 4
Rearrange to isolate V on the left hand side
The standard form of Ohm's law is V = IR, which holds for all ohmic conductors at constant temperature
A 20 Ξ© fixed resistor is connected directly to a 9 V battery. Calculate the current flowing through the resistor.
- 1
Start with the standard Ohm's law formula V = IR
- 2
Rearrange the formula to solve for unknown current I
- 3
- 4
Final answer: current flowing through the resistor is 0.45 A
4. V-I Characteristic Graphsβ β β βββ± 10 min
A V-I characteristic graph plots potential difference on the y-axis against measured current on the x-axis. For an ohmic conductor at constant temperature, this graph is a perfectly straight line passing through the origin. Non-ohmic components such as filament lamps and diodes produce curved V-I graphs, as their resistance changes with operating temperature or current direction.
Test your understanding of V-I graph properties:
What shape is the V-I graph for an ohmic conductor held at constant temperature?
Curved line through origin
Straight line through origin
Horizontal line
Vertical line
Reveal answer
Straight line through origin βOhmic conductors have constant resistance, so V is directly proportional to I, producing a straight line that passes through the origin.
5. Common Pitfalls
Wrong move:
Using the gradient of a non-ohmic V-I curve to calculate resistance at a point
Why:
The gradient gives dV/dI, not the actual definition of resistance V/I that IB exam mark schemes require
Correct move:
Divide the V coordinate by the I coordinate at the exact operating point you are measuring
Wrong move:
Forgetting to state that Ohm's law only applies at constant temperature
Why:
Heating a metallic conductor increases its resistance, breaking the proportionality between V and I
Correct move:
Always explicitly mention constant temperature when proving a component is ohmic in exam answers
Wrong move:
Connecting a voltmeter in series with a circuit component
Why:
Voltmeters have extremely high internal resistance, so almost no current will flow in the rest of the circuit
Correct move:
Always connect voltmeters in parallel across the two points you are measuring potential difference between
Wrong move:
Using mA directly instead of converting to A in Ohm's law calculations
Why:
1 mA = 0.001 A, so using mA directly will produce an answer 1000 times larger than the correct value
Correct move:
Convert all current values to amperes before substituting into V=IR
6. Quick Reference Cheatsheet
Quantity | Symbol | SI Unit | Core Formula |
|---|---|---|---|
Potential Difference | V | Volt (V) | |
Current | I | Ampere (A) | |
Resistance | R | Ohm (Ξ©) | |
Ohm's Law |
When this came up on past exams
AI-estimated based on syllabus patterns β cross-check with official past papers for accuracy. Use only as revision-focus signals.
- 2023 Β· Paper 1
Ohmic conductor multiple choice
- 2022 Β· Paper 2
Calculate resistance from V-I graph
- 2021 Β· Paper 2
Apply Ohm's law to series circuit
What's Next
Now that you have mastered the core definitions of potential difference, resistance and Ohm's law, you are ready to apply these concepts to more complex circuit arrangements. You will learn how to calculate total resistance for series and parallel resistor combinations, how to measure unknown resistance using practical circuits, and how to analyse the behaviour of non-ohmic components like diodes and thermistors in exam scenarios. These skills make up 15-20% of the IB Physics SL Paper 2 mark allocation, so regular practice with calculation questions will significantly boost your exam performance.