Investigating Current & Potential Difference
in an Electric Circuit
A practical guide for physics and engineering students — covering Ohm’s Law, how to set up the V-I experiment, how to plot and interpret your results, and how to calculate electric charge using Q = It. Plus: step-by-step guidance on writing up your lab report or assignment.
⚡ Need help with your electric circuits assignment, lab report, or physics coursework?
Get Expert Help →Core Concepts: Voltage, Current, Resistance, and Charge
When physicists investigate the relationship between current and potential difference in a circuit, they are testing one specific claim: that for a conductor at constant temperature, the current flowing through it is directly proportional to the potential difference across it. That claim is Ohm’s Law. The investigation either confirms it (if you get a straight line through the origin on your V-I graph) or challenges it (if you don’t). Everything else — the equipment, the method, the calculations, the graph analysis — serves that one purpose.
Before any experiment or assignment makes sense, four quantities need to be clear. Not vaguely familiar — actually clear. Because most errors students make in this topic trace back to mixing up what these quantities are, what units they use, and how they relate to each other.
The relationship between them is not complicated. Current is charge moving. Potential difference is what makes it move. Resistance is what slows it down. Most of the maths in this topic is just manipulating the two equations that connect these four quantities — V = IR and Q = It.
Potential Difference (Voltage)
The energy transferred per unit charge. Think of it as the electrical “pressure” that pushes current around. Measured with a voltmeter, connected in parallel.
Current
The flow of charge carriers (electrons in a wire). One ampere means one coulomb of charge passes per second. Measured with an ammeter, connected in series.
Resistance
How much a component resists current flow. High resistance = low current for a given voltage. Resistance is what you calculate from the gradient of your V-I graph.
Electric Charge
The total charge that flows through a circuit over time. If you know the current and how long it flows, you can calculate the charge: Q = It.
Ohm’s Law — What V = IR Actually Means
Ohm’s Law states that the potential difference across a conductor is directly proportional to the current flowing through it, provided the temperature remains constant. Written as a formula: V = IR.
That word “proportional” is doing a lot of work. It means: double the voltage, double the current. Halve the voltage, halve the current. The ratio V/I stays constant. That constant ratio is the resistance R. So you can rearrange the formula three ways depending on what you need to find:
The temperature condition matters more than most textbooks emphasise. Resistance in metal conductors increases with temperature. So if you run too much current through a resistor and it heats up mid-experiment, R changes — and Ohm’s Law appears to break down. It hasn’t broken down; the condition just isn’t being met. This is why your investigation should use low currents and take readings quickly.
Resistance (Ω) = Potential Difference (V) ÷ Current (A)
Given: V = 12 V | I = 0.5 A
R = 12 ÷ 0.5 = 24 Ω
Check: 24 Ω × 0.5 A = 12 V ✓ The resistor has a resistance of 24 ohms.
Current (A) = Potential Difference (V) ÷ Resistance (Ω)
Given: V = 9 V | R = 60 Ω
I = 9 ÷ 60 = 0.15 A
Check: 60 Ω × 0.15 A = 9 V ✓ A current of 0.15 amperes flows through the resistor.
The Triangle Trick — Use It, Then Move Past It
The V-I-R triangle (cover what you want to find; what’s left is the formula) is a useful memory tool at GCSE level. But at A-level and beyond, you need to be able to work from first principles — not just plug numbers in. Markers at higher levels look for evidence that you understand why the formula works, not just that you can use it. When writing up, always state what each variable represents and its unit before substituting values.
Electric Charge Calculation: Q = It — The Key Formula and How to Apply It
Electric charge (Q) is the total amount of electrical charge that passes through a point in a circuit over a period of time. The formula connecting charge, current, and time is one of the most straightforward in physics — and one of the most commonly misapplied, usually because of a unit conversion error with time.
Q = charge in coulombs (C) | I = current in amperes (A) | t = time in seconds (s)
Time MUST be in seconds. Convert minutes → seconds by multiplying by 60. Convert hours → seconds by multiplying by 3600.
1 coulomb = 1 ampere flowing for 1 second. That’s the physical meaning of the unit.
Identify: I = 2 A | t = 5 minutes — MUST convert to seconds first
Step 1 — Convert time: 5 minutes × 60 = 300 seconds
Step 2 — Substitute into Q = It:
Q = 2 A × 300 s = 600 C
Answer: 600 coulombs of charge pass through the resistor.
Physical interpretation: 600 coulombs is equivalent to approximately 3.75 × 10²¹ electrons — each carrying a charge of 1.6 × 10⁻¹⁹ C.
The single most common error on this type of question is using minutes instead of seconds. The formula Q = It only works when time is in seconds. If you put 5 into the formula instead of 300, you get 10 C — which is wrong by a factor of 60. Always convert time to seconds as your first step, before touching anything else. Write it down explicitly so it’s visible in your working.
More Worked Examples: Building Confidence With Q = It
Rearrange Q = It → t = Q ÷ I
Given: Q = 180 C | I = 3 A
t = 180 ÷ 3 = 60 seconds (1 minute)
Check: 3 A × 60 s = 180 C ✓
Rearrange Q = It → I = Q ÷ t
Step 1 — Convert time: 10 minutes × 60 = 600 seconds
I = 1500 ÷ 600 = 2.5 A
Check: 2.5 A × 600 s = 1500 C ✓
| Given | Find | Rearrangement | Example |
|---|---|---|---|
| I and t | Q (charge) | Q = I × t | I = 2 A, t = 300 s → Q = 600 C |
| Q and t | I (current) | I = Q ÷ t | Q = 900 C, t = 300 s → I = 3 A |
| Q and I | t (time) | t = Q ÷ I | Q = 480 C, I = 4 A → t = 120 s = 2 min |
The V-I Experiment: Circuit Setup, Equipment, and Method
This is the standard practical investigation used to verify Ohm’s Law. The goal is to vary the potential difference across a component systematically, measure the resulting current at each voltage, and then plot a V-I graph to see if the relationship is linear. Here is how to set it up properly.
Equipment You Need
| Equipment | Purpose | Connection |
|---|---|---|
| Variable DC power supply (or battery + rheostat) | Provides an adjustable potential difference across the circuit | Connected to the main circuit loop |
| Ammeter | Measures the current flowing through the component | In series — the current flows through it |
| Voltmeter | Measures the potential difference across the component | In parallel — it sits across the component being tested |
| Resistor (or other component under test) | The component whose V-I relationship you are investigating | In the main circuit loop |
| Connecting wires and switch | Complete the circuit; switch limits heating between readings | Switch in series with the component |
| Rheostat (variable resistor) | Allows fine control of current without changing the supply voltage | In series with the component under test |
The Ammeter and Voltmeter Positions Are Not Optional
The ammeter goes in series. The voltmeter goes in parallel. These are not stylistic choices — they follow from what each instrument measures. An ammeter measures current flowing through it, so it must be in the path the current takes. A voltmeter measures the potential difference between two points, so it connects across (in parallel with) whatever you are measuring. Swapping them blows ammeters and gives meaningless voltmeter readings. In your circuit diagram and your write-up, the instrument positions must be explicitly correct.
Method: How to Run the Investigation
Build and Check the Circuit
Assemble the circuit with the ammeter in series and the voltmeter in parallel across the resistor. Before switching on, check all connections. Keep the switch open until you are ready to take a reading — leaving it closed heats the resistor and changes its resistance.
Set Your First Voltage and Take the Reading
Close the switch. Set the supply to your first voltage (e.g., 1 V). Read the ammeter quickly and record both V and I. Open the switch immediately. Record your data in a table with columns for Voltage (V), Current (A), and Resistance R = V/I (Ω).
Repeat Across a Range of Voltages
Increase the voltage in regular steps (e.g., 1 V, 2 V, 3 V, 4 V, 5 V). Take a reading at each step. A minimum of six to eight data points gives you enough to draw a meaningful graph. For greater reliability, take repeat readings and average them.
Reverse the Connections (If Required)
For a complete V-I characteristic (especially if the component is a diode or bulb), reverse the battery connections to get negative voltage readings. This gives you a symmetric graph around the origin for ohmic conductors.
Plot Your V-I Graph and Calculate Resistance
Plot potential difference (V) on the y-axis and current (I) on the x-axis. Draw a line of best fit. For an ohmic resistor it will be straight and pass through the origin. The gradient of the line = R (resistance in ohms).
Why Plot V on the y-Axis and I on the x-Axis?
Convention — and your mark scheme — typically puts V on the y-axis and I on the x-axis. The gradient of this graph gives R directly (since V = IR means gradient = R). Some textbooks reverse this (I on y, V on x), in which case the gradient gives 1/R (conductance). Check your exam board’s specification. If it says “V-I graph,” put V on the vertical axis. If it says “I-V graph,” put I on the vertical axis. The physics is the same; only the gradient interpretation changes.
Plotting and Interpreting the V-I Graph
The graph is where the investigation either confirms or challenges Ohm’s Law. Getting the data collection right matters less if you cannot correctly read what the graph is telling you. Here is what to look for and how to describe it.
| Graph Shape | What It Means | Component Type | How to Calculate R |
|---|---|---|---|
| Straight line through the origin | V is directly proportional to I. Ohm’s Law holds. Resistance is constant. | Ohmic conductor (e.g., metal resistor at constant temperature) | R = gradient = ΔV ÷ ΔI (pick two widely spaced points on the line) |
| Curve that flattens at higher currents | Resistance is increasing as current increases. Temperature is rising, increasing resistance. | Filament lamp (non-ohmic) | R at any point = V ÷ I at that specific point (not the gradient) |
| Asymmetric — conducts in one direction only | Very low resistance in forward bias; very high resistance in reverse bias. | Diode (non-ohmic) | R = V ÷ I at any point, but varies enormously with direction |
| Straight line but NOT through origin | There is a systematic error in the experiment — usually an offset in one of the meters, or contact resistance in the circuit. | Could be any component — indicates measurement issue | Investigate the anomaly; do not force the line through the origin |
Two points: (0, 0) and (0.4, 8)
Gradient = (8 − 0) ÷ (0.4 − 0) = 8 ÷ 0.4 = 20 Ω
The resistor has a resistance of 20 ohms. Verify: V = IR → 0.4 A × 20 Ω = 8 V ✓
The graph does not just show you the answer — it shows you whether the answer is trustworthy. A straight line through the origin with small scatter around it tells you the experiment was well-controlled. A curved or scattered set of points tells you something changed that shouldn’t have.
— Standard guidance in A-level Physics practical skillsWhat to Write in Your Analysis Section
Three things belong in the analysis of a V-I investigation. First, describe the shape of the graph precisely — do not say “the graph shows the relationship between V and I.” Say whether it is linear, whether it passes through the origin, and whether there are any anomalies. Second, state what the shape tells you about the component (ohmic or non-ohmic, and why). Third, calculate the resistance — either from the gradient (for linear graphs) or from individual V/I pairs (for curves). All three need to be in your write-up to get full marks at any level.
Ohmic vs. Non-Ohmic Components — What the Difference Means
An ohmic conductor is one that obeys Ohm’s Law — its resistance stays constant regardless of the current flowing through it (as long as temperature stays constant). A non-ohmic component has a resistance that changes as conditions change. The distinction is not just exam content; it tells you which components are predictable to use in circuit design and which are not.
Ohmic Conductors
- Straight V-I graph through the origin
- Constant resistance at constant temperature
- Metal wires, most standard resistors
- V and I increase proportionally
- R can be calculated from gradient
- Temperature must stay constant for the law to hold
Non-Ohmic Components
- Curved V-I graph (filament lamp) or asymmetric (diode)
- Resistance changes with current, temperature, or light
- Filament lamps, diodes, thermistors, LDRs
- V and I do not increase proportionally
- R must be calculated as V/I at each specific point
- Their changing resistance is often the useful property (e.g., thermistors in temperature sensors)
Why Filament Lamps Are Non-Ohmic: The Temperature Explanation
A filament lamp contains a thin tungsten wire. At low voltages, the wire is cool and its resistance is relatively low. As voltage increases, more current flows, the wire heats up — it can reach temperatures above 2,500°C — and resistance increases significantly. So each time you increase the voltage, you get less current than Ohm’s Law would predict for a fixed resistance. The V-I graph curves away from a straight line. The resistance at operating temperature can be ten to fifteen times higher than the cold resistance. This is confirmed in published data from sources such as the Institute of Physics, which maintains extensive practical physics resources for exactly this type of investigation.
Common Mistakes Students Make in V-I Investigations
These are the errors that show up repeatedly in marked scripts and practical reports. Some are experimental. Some are calculation errors. Most are avoidable if you know to watch for them.
| Error | Why It Happens | How to Avoid It |
|---|---|---|
| Using minutes instead of seconds in Q = It | Time is given in minutes in the question; students forget to convert | Always convert time to seconds as the first written step. Write “t = ___ min × 60 = ___ s” before substituting |
| Putting the ammeter in parallel and the voltmeter in series | Confusion about what each instrument measures and where it goes | Ammeter = in series (measures current through it). Voltmeter = in parallel (measures potential difference across). No exceptions. |
| Calculating gradient using single points instead of two widely spaced points | Students pick any two adjacent data points or use a single point divided by the x-axis value | Use two points far apart on the line of best fit (not data points). Show the triangle on your graph with ΔV and ΔI labelled. |
| Saying “the graph shows Ohm’s Law is obeyed” without explaining why | Students state the conclusion without the evidence | State: the graph is a straight line passing through the origin, which shows V is directly proportional to I, confirming Ohm’s Law at constant temperature |
| Leaving the switch closed between readings | Students don’t realise the continuous current heats the resistor | Open the switch between each reading. Only close it while taking the measurement. This keeps temperature approximately constant. |
| Mixing up R = V/I with R = ΔV/ΔI | For ohmic conductors both give the same answer, so the difference isn’t obvious until a non-ohmic component is used | For ohmic: use the gradient (ΔV/ΔI). For non-ohmic: use V/I at each specific point — the gradient of a tangent, not the overall slope. |
Writing Up Your Lab Report or Assignment: Section by Section
Whether this is a formal lab report, a coursework write-up, or a structured assignment question, the same core structure applies. Each section has a specific job. Get the structure right first, then fill in the physics. If you need expert support with your physics assignment or lab report, Smart Academic Writing’s science specialists can help at all levels.
Title and Aim
Short and precise — states exactly what is being investigated
State the investigation clearly. Example: “To investigate the relationship between potential difference and current in an ohmic conductor, and to determine its resistance.” One sentence is enough. Do not pad it. Avoid vague aims like “to learn about circuits” — the aim should be measurable and specific.
Hypothesis / Prediction
What do you expect to find, and why?
State your prediction based on theory. Example: “I predict that the current through the resistor will be directly proportional to the potential difference across it, in accordance with Ohm’s Law (V = IR), provided the temperature remains constant. This means the V-I graph will be a straight line passing through the origin, with the gradient equal to the resistance.”
The key is “and why.” A hypothesis without a theoretical basis gets half credit at best. Cite Ohm’s Law by name, state the formula, and link it to the expected graph shape.
Method
Reproducible, specific, and honest about controls
List equipment with specifications (e.g., “digital ammeter, range 0–2 A, resolution 0.01 A”). Draw a circuit diagram using standard IEC/BS symbols — not a photograph of the actual circuit. Write the procedure in steps that someone else could follow to reproduce the experiment exactly.
State your independent variable (potential difference — what you change), dependent variable (current — what you measure), and controlled variables (temperature, same resistor, same connections throughout). This is what markers look for when assessing experimental design.
Results Table
Organised, correctly headed, with units
Set out a table with: Voltage V (V) | Current I (A) | Resistance R = V/I (Ω). If you took repeat readings, include a column for each repeat and a mean. Units go in the column heading, not in the data cells. Data should be recorded to a consistent number of decimal places that matches your instrument resolution.
Identify any anomalous results. Don’t delete them — mark them clearly and exclude them from your graph and mean calculations, then explain in your evaluation why they are anomalous.
Graph
Correctly axes, scaled, and interpreted
V on the y-axis, I on the x-axis. Label both axes with quantity and unit. Scale them so the data occupies at least half the graph area — do not squash everything into one corner. Plot all points. Draw a line of best fit (straight or curved, as the data demands — never connect the dots). Mark any anomalous points clearly but do not include them in the best fit line.
Calculate the gradient: show the triangle on the graph with ΔV and ΔI labelled. State R = gradient = ___ Ω. If the graph is curved (non-ohmic), calculate R at several specific points using R = V/I.
Analysis and Conclusion
Link the data back to the physics
State clearly: (a) what the graph shows — describe the shape and whether it is linear; (b) what this means for Ohm’s Law — does the component obey it or not, and how do you know from the graph; (c) the calculated resistance with units; (d) whether the result matches your hypothesis, and if not, why not.
Do not just repeat the results. Interpret them. “The straight line through the origin shows that V is directly proportional to I. This confirms that the resistor is an ohmic conductor and that Ohm’s Law holds at constant temperature. The resistance, calculated from the gradient, is 24 Ω.”
Evaluation
Honest assessment of errors, limitations, and improvements
This section is where most students lose marks — either by saying nothing or by listing generic statements like “human error.” Be specific. Identify: systematic errors (e.g., voltmeter draws a small current, causing the ammeter to overread); random errors (e.g., fluctuation in power supply voltage between readings); and limitations (e.g., only six data points — more would give greater confidence in the linear relationship).
For each error, suggest a specific improvement. “Using a higher-impedance voltmeter would reduce the current drawn by the voltmeter itself, improving accuracy.” Examiners want evidence that you understand the physics behind the errors, not just that errors exist.
What Distinguishes a Top-Mark Write-Up
- The hypothesis cites the theory — Ohm’s Law is stated with the formula, not just described vaguely
- The circuit diagram uses standard symbols — ammeter in series, voltmeter in parallel, clearly labelled
- Variables are explicitly identified — independent, dependent, and all controlled variables stated
- The graph gradient is calculated correctly — large triangle, showing ΔV and ΔI, not using single points
- The conclusion links back to Ohm’s Law — not just “it was a straight line” but what that line means physically
- The evaluation identifies specific, named errors — not generic “human error” statements
FAQs: Current, Potential Difference, and Electric Charge
Bringing It Together: What This Investigation Is Really Testing
The V-I investigation looks simple on the surface — connect a resistor, vary the voltage, measure the current, plot a graph. But the marks, at every level, go to students who show they understand the physics behind the procedure. Why is the ammeter in series? Because that’s what measuring current requires. Why does the graph need to pass through the origin? Because V = IR means V = 0 when I = 0. Why must temperature be controlled? Because resistance depends on temperature, and changing R would break the proportionality Ohm’s Law predicts.
The charge calculation follows the same principle. Q = It is a simple formula. But applying it correctly means knowing to convert time to seconds first — every time, without exception. That one step separates a correct answer from one that’s wrong by a factor of 60.
If you need expert support with your physics assignment, lab report, or electric circuits coursework, the science writing team at Smart Academic Writing can help — through academic writing services, lab report writing, and subject-specific homework help across physics, chemistry, and biology.