IV graphs for ohmic resistors, filament bulbs and diodes; calculating resistance from gradient
📈 Describe the shape of an IV graph for an ohmic resistor and explain why it is a straight line through the origin
💡 Describe the shape of an IV graph for a filament lamp and explain the curve in terms of temperature and resistance
⚡ Describe the IV graph for a diode, including threshold voltage and reverse bias
🔢 Calculate resistance from the gradient of an IV graph using R = V ÷ I
🔬 Describe the required practical method for measuring IV characteristics safely
⚙️ Interpret and sketch IV graphs, identifying key features for each component
Ohm's Law and the IV Graph
Ohm's Law states that the current through a conductor is directly proportional to the potential difference across it, provided the temperature remains constant. This relationship is written as:
V = I × R
Where V is potential difference in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω).
Symbol
Quantity
Unit
V
Potential difference
Volts (V)
I
Current
Amperes (A)
R
Resistance
Ohms (Ω)
An ohmic conductor is one that obeys Ohm's Law — its resistance stays constant as the current changes (at constant temperature).
On an IV graph (current on the y-axis, voltage on the x-axis), an ohmic resistor produces a straight line through the origin. The steeper the line, the lower the resistance — more current flows for the same voltage. Rearranging Ohm's law shows us:
R = V ÷ I
Because the line is straight through the origin, the gradient of the line equals I ÷ V, which is 1 ÷ R. So resistance = 1 ÷ gradient. A steeper IV graph means lower resistance. Importantly, the graph is symmetric — if you reverse the voltage, the same current flows in the opposite direction.
For an ohmic resistor: straight line through the origin. Resistance = 1 ÷ gradient of the IV graph.
Filament Lamp IV Characteristics
A filament lamp does not obey Ohm's Law. Its IV graph is a curved line that starts steep (high gradient, low resistance) and then flattens out as voltage increases.
Why does this happen? As more current flows through the thin tungsten filament wire, it gets much hotter — sometimes reaching temperatures over 2000°C when fully lit. This increasing temperature causes the metal ions in the wire to vibrate more vigorously, making it harder for electrons to pass through. This means the resistance of the filament lamp increases as the temperature rises.
A non-ohmic conductor does not have a constant resistance — its resistance changes with conditions such as temperature or light level.
On the IV graph for a filament lamp:
At low voltages, the gradient is steep → resistance is low (filament is cool)
As voltage increases, the gradient decreases → resistance increases (filament heats up)
The curve is symmetric about the origin — reversing the voltage has the same effect
For a filament lamp: S-shaped curve through the origin. Resistance increases with temperature as the filament heats up.
To find resistance at any point on the curve, pick that point and calculate R = V ÷ I using the coordinates of that specific point (NOT the gradient of the tangent). The gradient approach only works for straight lines.
Diode IV Characteristics
A diode is a component that only allows current to flow in one direction. Its IV graph looks very different from both a resistor and a filament lamp.
A diode is a semiconductor device that conducts current in only one direction, making it useful for converting alternating current (AC) to direct current (DC).
Key features of the diode IV graph:
Forward bias (positive voltage): Very little current flows until the voltage reaches the threshold voltage (about 0.7 V for a silicon diode). Above this voltage, current rises steeply — resistance is very low.
Reverse bias (negative voltage): Virtually no current flows — the resistance is extremely high. The graph shows a near-flat line just below zero on the current axis.
Threshold voltage for a silicon diode ≈ 0.7 V. Below this in forward bias, and in all of reverse bias, almost no current flows.
The IV graph for a diode is not symmetric — it behaves completely differently depending on which way the voltage is applied. This asymmetry is the key distinguishing feature of a diode.
In forward bias (V > 0.7 V): very low R — large I flows In reverse bias (V < 0): very high R — I ≈ 0
Diodes are widely used in rectifier circuits to ensure current only flows one way, protecting sensitive electronic components. LEDs (Light Emitting Diodes) work on the same principle but emit light when current flows through them in forward bias.
Calculating Resistance from an IV Graph
No matter which component you are analysing, resistance is always found using:
R = V ÷ I
How you apply this depends on the shape of the IV graph:
For ohmic resistors (straight line):
The resistance is constant everywhere. You can use any point on the line, or use the gradient:
gradient = I ÷ V = 1 ÷ R → R = 1 ÷ gradient
For non-ohmic components (curved line):
Resistance changes at every point. To find R at a specific point, read off the V and I coordinates of that exact point, then calculate:
R = V ÷ I (using coordinates of the chosen point)
Do not use the gradient of a tangent on a curved IV graph to find resistance — this does not give you V ÷ I at that point.
Always: R = V ÷ I. For a straight-line graph, R = 1 ÷ gradient. For a curved graph, use the coordinates of the specific point of interest.
Component
IV Graph Shape
Resistance
Ohmic resistor
Straight line through origin
Constant
Filament lamp
Curve (S-shape), symmetric
Increases with temperature
Diode
Asymmetric — conducts only forward
Very high in reverse; very low above threshold
Example 1: Calculating resistance from a straight-line IV graph
A resistor's IV graph shows that when the voltage is 6.0 V, the current is 0.30 A. The graph is a straight line through the origin. Calculate the resistance of the resistor.
1Identify the values from the graph: V = 6.0 V, I = 0.30 A
2Write the equation: R = V ÷ I
3Substitute: R = 6.0 ÷ 0.30
4Calculate: R = 20 Ω
Resistance = 20 Ω
Example 2: Resistance from gradient of IV graph
A student plots an IV graph for a fixed resistor. The gradient of the straight line is 0.050 A/V. Calculate the resistance.
1For a straight-line IV graph, the gradient = I ÷ V = 1 ÷ R
2So: R = 1 ÷ gradient
3Substitute: R = 1 ÷ 0.050
4Calculate: R = 20 Ω
Resistance = 20 Ω
Example 3: Resistance of a filament lamp at a specific point
From a filament lamp's IV graph, at one operating point the voltage is 4.0 V and the current is 0.080 A. At another operating point the voltage is 8.0 V and the current is 0.100 A. Calculate the resistance at each point and explain what this tells you.
1At point 1: R = V ÷ I = 4.0 ÷ 0.080 = 50 Ω
2At point 2: R = V ÷ I = 8.0 ÷ 0.100 = 80 Ω
3Compare the two values: 50 Ω at lower voltage, 80 Ω at higher voltage
4Explain: As voltage (and current) increases, the filament gets hotter. Higher temperature causes greater resistance because the metal ions vibrate more vigorously, impeding electron flow more.
Resistance at 4.0 V = 50 Ω; Resistance at 8.0 V = 80 Ω. Resistance increases with temperature — the lamp is non-ohmic.
Example 4: Describing a diode IV graph
A student connects a diode in a circuit and records current and voltage data. Describe what the IV graph looks like and explain what happens when the voltage is: (a) below the threshold voltage in forward bias, (b) above the threshold voltage, and (c) in reverse bias.
1(a) Below threshold voltage (e.g., 0 V to ~0.7 V in forward bias): Almost no current flows. The resistance of the diode is very high. The graph is nearly flat near zero current.
2(b) Above threshold voltage (~0.7 V for silicon): Current increases rapidly and steeply. The resistance of the diode drops to a very low value, allowing large currents to flow.
3(c) In reverse bias (negative voltage): Almost no current flows in the reverse direction. The resistance is extremely high. The graph shows a near-flat line just below the x-axis.
4Overall shape: The graph is NOT symmetric. In forward bias above 0.7 V it rises sharply; in reverse bias it stays near zero. This asymmetry is the defining feature of a diode.
Below threshold: near-zero current, high resistance. Above 0.7 V: rapid current rise, low resistance. Reverse bias: near-zero current, extremely high resistance. Graph is asymmetric.
Question 1: Which statement best describes an ohmic conductor?
✅ Correct! An ohmic conductor has I directly proportional to V at constant temperature — its IV graph is a straight line through the origin.
Question 2: A resistor has a voltage of 9.0 V across it and a current of 0.45 A flowing through it. What is its resistance?
Question 3: Why does the resistance of a filament lamp increase as it gets hotter?
✅ Correct! At higher temperatures, metal ions in the filament vibrate with greater amplitude, impeding the flow of electrons and increasing resistance.
Question 4: The gradient of a straight-line IV graph is 0.025 A/V. What is the resistance of the component?
Question 5: What happens to the current through a diode when the voltage is reversed (reverse bias)?
✅ Correct! In reverse bias, the diode has an extremely high resistance and virtually no current flows. This is what makes diodes useful for controlling current direction.
Challenge 1 (6 marks): A student investigates two resistors, A and B, by plotting IV graphs. Resistor A has a gradient of 0.10 A/V. Resistor B has a gradient of 0.040 A/V.
(a) Calculate the resistance of each resistor. (b) If both resistors are connected in series with a 12 V battery, calculate the total resistance and the current in the circuit.
(a)
R_A = 1 ÷ 0.10 = 10 Ω
R_B = 1 ÷ 0.040 = 25 Ω
(b)
Total resistance in series: R_total = R_A + R_B = 10 + 25 = 35 Ω
Current: I = V ÷ R = 12 ÷ 35 = 0.34 A (2 s.f.)
Challenge 2 (5 marks): The table below shows data points from an IV graph for a filament lamp:
V = 2.0 V, I = 0.050 A
V = 4.0 V, I = 0.080 A
V = 6.0 V, I = 0.10 A
V = 8.0 V, I = 0.11 A
(a) Calculate the resistance at each voltage.
(b) Describe how resistance changes as voltage increases and explain why in terms of the filament's temperature.
(a)
At 2.0 V: R = 2.0 ÷ 0.050 = 40 Ω
At 4.0 V: R = 4.0 ÷ 0.080 = 50 Ω
At 6.0 V: R = 6.0 ÷ 0.10 = 60 Ω
At 8.0 V: R = 8.0 ÷ 0.11 = 73 Ω (2 s.f.)
(b) Resistance increases as voltage increases. As voltage increases, more current flows, which heats the filament to a higher temperature. At higher temperatures, the metal ions in the tungsten filament vibrate with greater amplitude, making it more difficult for electrons to pass through. This increased collision frequency between electrons and vibrating ions results in a higher resistance. The lamp is a non-ohmic conductor.
Challenge 3 (4 marks): Sketch and describe the IV graph for a diode. Your answer must include: the approximate threshold voltage, what happens in forward bias below and above this voltage, what happens in reverse bias, and why the graph is described as asymmetric.
Model Answer:
The IV graph for a diode is asymmetric about the origin.
Forward bias below threshold (~0.7 V): The current is almost zero. The diode has a very high resistance and does not conduct significantly.
Forward bias above threshold (~0.7 V for silicon): The current rises steeply and quickly. The resistance drops to a very low value, allowing large currents to flow. The graph curves sharply upward.
Reverse bias (negative voltage): Almost no current flows regardless of how negative the voltage is. The graph remains near zero — essentially a flat line just below the x-axis. The resistance is extremely high.
Why asymmetric: Unlike a resistor or filament lamp whose graphs are symmetric about the origin, the diode behaves completely differently in forward and reverse bias. This is because of its semiconductor structure — it only allows current in one direction.
Challenge 4 — Extended Response (6 marks): A student is given three components: an ohmic resistor, a filament lamp, and a diode. They plot IV graphs for each component using the same axes (voltage from −10 V to +10 V). Compare and contrast the three IV graphs, including the shape, symmetry, and what each graph tells us about the resistance of the component.
Model Answer (6 marks):
Ohmic resistor: The IV graph is a straight line passing through the origin. It is symmetric — applying voltage in either direction gives the same magnitude of current. The straight line indicates constant resistance (R = V ÷ I is the same at all points). The gradient of the line equals 1 ÷ R.
Filament lamp: The IV graph is a smooth curve through the origin, symmetric about the origin. At low voltages the curve is steep (low resistance, cool filament), but it flattens as voltage increases (higher resistance as filament heats up). The increasing resistance with temperature makes it a non-ohmic component. To find resistance at a point, use R = V ÷ I with the coordinates of that point.
Diode: The IV graph is asymmetric. In forward bias, almost no current flows below ~0.7 V (high resistance), then current rises sharply above 0.7 V (very low resistance). In reverse bias (negative voltage), almost no current flows at all — resistance is extremely high. The graph does not cross the origin in the same way as the other two — it is distinctly different on either side of the origin.
Key comparison: The resistor has constant, predictable resistance. The filament lamp has increasing resistance with temperature. The diode has a resistance that depends dramatically on both the magnitude and direction of the applied voltage. All three have very different shaped IV graphs that reflect their different physical behaviours.
🔬 Required Practical — AQA GCSE Physics 4.2
Measuring IV Characteristics
In this required practical, you will measure the current through and voltage across three components — a fixed resistor, a filament lamp, and a diode — to plot their IV characteristic graphs.
Equipment Required
Variable power supply (or variable resistor/rheostat)
Voltmeter (connected in parallel with the component)
Connect the ammeter in series with the component (measures current through it)
Connect the voltmeter in parallel with the component (measures voltage across it)
Use the variable power supply or rheostat to gradually change the voltage from 0 V upwards
For the diode only: include a protective resistor (e.g., 100 Ω) in series to prevent damage from excessive current
To get negative voltage readings, reverse the connections to the power supply
Method
Set up the circuit with the fixed resistor first
Set the voltage to 0 V using the variable supply
Gradually increase the voltage in steps (e.g., 1 V intervals) up to the maximum safe value
Record the voltmeter reading (V) and ammeter reading (I) at each step
Reverse the connections to obtain readings at negative voltages
Repeat for the filament lamp and then the diode
For the diode, also test forward voltages from 0 V to about 1.0 V in small steps (0.1 V) around the threshold
Plot IV graphs for all three components — put voltage (V) on the x-axis and current (I) on the y-axis
Safety Considerations
⚠️ Never exceed the maximum rated voltage or current for any component — check component ratings before starting
⚠️ The filament lamp will get very hot — do not touch it during or immediately after the experiment
⚠️ Always include a protective resistor in series with the diode to prevent damage from excess current
⚠️ Turn off the power supply between taking readings if the components are getting excessively hot
⚠️ Check all connections before switching on the supply
Results Table
Voltage V (V)
Current I — Resistor (A)
Current I — Lamp (A)
Current I — Diode (A)
−6.0
≈ 0
−4.0
≈ 0
−2.0
≈ 0
0.0
0
0
0
+0.5
≈ 0
+0.7
Starts to flow
+1.0
+2.0
+4.0
+6.0
Analysis Questions
A1: What shape do you expect for the resistor's IV graph? What does this tell you about its resistance?
A straight line through the origin — this shows the resistor is ohmic with a constant resistance. The resistance can be calculated using R = 1 ÷ gradient.
A2: How does the shape of the filament lamp's IV graph differ from the resistor's? Explain why in terms of resistance and temperature.
The filament lamp's graph is a curve that flattens as voltage increases (an S-shape). Unlike the straight line of the resistor, this shows the resistance is increasing. As current increases, the filament gets hotter, causing the metal ions to vibrate more vigorously, increasing resistance.
A3: Using your results, calculate the resistance of the fixed resistor at a voltage of your choice. Show your working.
Example: If V = 4.0 V and I = 0.20 A → R = V ÷ I = 4.0 ÷ 0.20 = 20 Ω. Accept any valid calculation using the student's own data.
A4: What is the approximate threshold voltage of the diode you tested? How can you identify this from the IV graph?
For a silicon diode, the threshold voltage is approximately 0.6–0.7 V. On the IV graph, this is the voltage at which the current begins to rise sharply in forward bias — the point where the graph curves steeply upward from near-zero current.