Investigate the current-voltage behaviour of ohmic resistors, filament lamps, diodes, and thermistors β and explain the physics behind each graph shape.
AQA A-Level Physics Β· Unit 5: Electricity
πOhmic resistor Describe and explain the linear IV graph
π‘Filament lamp Explain the curved IV graph due to temperature
π΄Diode Describe the IV graph with threshold voltage and reverse bias
π‘οΈThermistor (NTC) Explain how resistance changes with temperature
π¬Practical skills Describe how to measure IV characteristics safely
πGraph interpretation Extract resistance R = V/I from any IV graph at a given point
Ohmic Resistor
An ohmic conductor (e.g. a fixed resistor at constant temperature) follows Ohm's law: current is directly proportional to p.d.
IV graph shape: A straight line through the origin. The gradient = I/V = 1/R. The steeper the line, the lower the resistance.
What happens as V is increased: Current increases proportionally. The ratio V/I remains constant β the resistance does not change.
An ohmic conductor has a constant resistance at constant temperature. Its IV graph is a straight line through the origin. R = V/I = constant.
Examples of approximately ohmic conductors: metallic resistors at room temperature, carbon resistors, some alloys (e.g. nichrome, manganin β used in precision resistors because their resistance changes very little with temperature).
For any IV graph, the resistance at a given point can be found as R = V/I, regardless of whether the component is ohmic. For non-ohmic components, this gives the resistance at that particular operating point.
Filament Lamp
A filament lamp contains a coiled tungsten wire. As the current increases, the wire heats up significantly (to ~2700 K when glowing).
IV graph shape: An S-shaped curve. The gradient (I/V = 1/R) decreases as V increases β meaning resistance increases with increasing voltage/current.
Why the curve flattens: As current increases β filament temperature increases β more lattice vibrations β more electron scattering β resistance increases β current increases less than proportionally with voltage.
Filament lamp: non-ohmic. Resistance increases with temperature (and therefore with current). The IV graph curves away from a straight line β it is steeper at low V (when the filament is cool) and flatter at high V (when it is hot).
The graph is symmetrical about the origin: same magnitude of current for same magnitude of voltage in either direction (the filament heats equally regardless of direction).
A semiconductor diode allows current to flow in one direction only. It is made from a p-n junction.
IV graph shape: Very different in forward and reverse bias:
Forward bias: Almost no current flows until the threshold (forward voltage) is reached β typically ~0.6β0.7 V for silicon. Beyond the threshold, current increases very steeply and exponentially.
Reverse bias: Virtually no current flows (a tiny leakage current). The diode appears to have effectively infinite resistance. At very large reverse voltage, the diode undergoes avalanche breakdown β not examined at A-level.
Threshold voltage: The minimum forward voltage required before a diode conducts significantly. For silicon diodes: approximately 0.6β0.7 V.
Applications of diodes: rectification (converting AC to DC), signal clipping, light-emitting diodes (LEDs), photodiodes (in reverse bias as light detectors).
The extremely steep rise after threshold means the diode has a very low resistance in forward bias (once conducting) and a very high resistance in reverse bias.
Thermistor (NTC)
An NTC (negative temperature coefficient) thermistor is a semiconductor device whose resistance decreases significantly as temperature increases.
IV graph shape: If the thermistor is in a circuit where passing current heats it, the IV graph curves upward β current increases faster than linearly with voltage, because heating reduces resistance and allows more current. This is the opposite of a filament lamp's behaviour.
Why resistance decreases with temperature: The thermistor is a semiconductor. As temperature increases, more electrons gain sufficient thermal energy to enter the conduction band, increasing the number density n of charge carriers. From I = nAvq, more carriers β lower resistance for the same applied voltage.
NTC thermistor: Resistance decreases as temperature increases. Used in temperature sensors, thermostats, and self-resetting overcurrent protection.
Thermistors are used in temperature-dependent voltage divider circuits. As temperature rises, the thermistor resistance falls, changing the voltage across it β this signal can be used to trigger a thermostat or heating/cooling control.
LDR (Light Dependent Resistor): Similar principle β a semiconductor whose resistance decreases as light intensity increases (more photons β more free electron-hole pairs). Used in automatic lighting controls.
Thermistor (NTC) and LDR are both semiconductors whose resistance decreases as the activating stimulus (temperature/light) increases. This is opposite to metals.
From an IV graph of a filament lamp, at V = 2.0 V the current is 0.40 A, and at V = 6.0 V the current is 0.75 A. Calculate the resistance at each operating point and explain the difference.
1Voltage across resistor = supply voltage β diode threshold = 5.0 β 0.65 = 4.35 V
2Current I = V_R / R = 4.35 / 470 = 9.26 Γ 10β»Β³ A
I = 9.26 mA
Sketch the shape of the IV graph for (a) a resistor obeying Ohm's law, (b) a filament lamp, (c) a diode. Describe the key features of each.
1(a) Ohmic resistor: straight line through origin; constant gradient; R = 1/gradient = constant.
2(b) Filament lamp: curve through origin, symmetric; starts steep (low R when cool) then flattens (high R when hot). R increases with V.
3(c) Diode: in reverse bias, I β 0 for all negative V; in forward bias, I β 0 until threshold (~0.65 V), then rises very steeply. Shape resembles the letter "J" on its side.
See descriptions above. Key: ohmic = linear; filament = symmetric S-curve; diode = J-shape with threshold.
Q1. The IV graph of a filament lamp curves away from a straight line. What does this tell us about its resistance as voltage increases?
Q2. A diode is connected in reverse bias. Which best describes its behaviour?
Q3. An NTC thermistor is heated. What happens to (a) its resistance and (b) the current through it if the applied voltage is kept constant?
Q4. From an IV graph, the current at V = 3.0 V is 0.12 A. What is the resistance of the component at this operating point?
Q5. Explain why a cold filament lamp draws more current per volt than a hot one, even though the same voltage is applied.
Challenge Q2. A diode has the following IV data in forward bias: at V = 0.60 V, I = 2 mA; at V = 0.65 V, I = 20 mA; at V = 0.70 V, I = 80 mA. Calculate the resistance of the diode at each operating point and explain why these values decrease as V increases.
π¬ Required Practical Measure IV characteristics of a resistor, filament lamp, diode, and thermistor
Aim
To measure and compare the current-voltage (IV) characteristics of four different electrical components: a resistor, a filament lamp, a diode, and a thermistor.
Circuit Setup
Use a variable voltage power supply (or potential divider circuit) so that V can be varied from 0 upward. For each component:
Connect ammeter in series with the component and voltmeter in parallel across it.
Vary V from 0 to maximum in steps. Record I at each V.
For the diode only: repeat with reversed connections to measure reverse bias behaviour.
For the thermistor: use low voltages to prevent self-heating (or immerse in a water bath to control temperature).
Safety
Do not exceed the rated voltage of any component. Filament lamp filaments can reach very high temperatures β do not touch. Diodes are easily damaged by excess reverse voltage or current above forward rating. Keep currents low for thermistors to prevent self-heating if investigating resistance-temperature relationship.
Expected Graph Shapes
Resistor: Straight line through origin (both forward and reverse)
Filament lamp: Curve through origin, symmetric, flattening at higher V
Diode: Near-zero current for all reverse V; sharp increase above ~0.65 V in forward bias
Thermistor: Curve that steepens with V (if self-heating); or use resistance-temperature graph if temperature controlled
Analysis Questions
Why is a potential divider used instead of a simple series resistor when measuring the IV characteristic of a diode?