I-V Characteristics

Spec mapping: OCR H556 Module 4.2 — Energy, power and resistance (I-V characteristics for fixed resistor, filament lamp, semiconductor diode including LED, NTC thermistor, and LDR; sketching the curves; physical explanations for each shape; PAG 4 — investigating the I-V characteristic of a component). Refer to the official OCR H556 specification document for exact wording.

An I-V characteristic is a graph of current $I$I against potential difference $V$V for a particular component. It is the electrical "fingerprint" of a device — look at the shape of the curve and you can identify, often instantly, whether you are dealing with an ohmic resistor, a filament lamp, a semiconductor diode, a thermistor or an LDR. Each has a canonical shape determined by its underlying physics.

This lesson is one of OCR's most heavily-examined topics. PAG 4 explicitly requires you to experimentally measure an I-V characteristic; written exam questions ask you to sketch the curves, interpret data, and explain the physical mechanisms behind each shape. You should be able to do all three at the end of this lesson.

We cover the five canonical components in order, give worked examples of how to interpret real-looking data, and end with a specimen question that combines sketching, interpretation, and PAG-4 experimental design.

---

Experimental Setup — the PAG 4 Apparatus

To measure an I-V characteristic you need (i) a smoothly variable pd that can be swept from zero (and ideally into the reverse direction), and (ii) a way to measure $V$V and $I$I simultaneously. The standard A-Level apparatus uses:

• A potential divider (lesson 12) — not a rheostat. A rheostat in series with the component can only reduce the current; it cannot bring the pd to zero. The potential divider can.
• An ammeter in series with the component (zero-resistance ideal).
• A voltmeter in parallel across the component (infinite-resistance ideal).
• A switch to reverse the supply (to access negative-$V$V region).

flowchart LR
  B[Battery / variable supply] --> PD[Potential divider]
  PD --> A1((Ammeter))
  A1 --> DUT["Device under test"]
  DUT --> B
  DUT -.- V1((Voltmeter))

The pd is swept from a negative value through zero to a positive value, and at each setting both $V$V (from the voltmeter) and $I$I (from the ammeter) are recorded. Repeat readings are taken and averaged. Plot $I$I on the vertical axis against $V$V on the horizontal axis (the standard physics convention; see lesson 5).

OCR exam tip: When asked to "describe an experiment to investigate the I-V characteristic of a component", a full mark-scheme answer typically requires: (a) potential divider (not rheostat) to provide variable pd from zero; (b) ammeter in series; (c) voltmeter in parallel; (d) reversing the connections to access negative-V region; (e) repeat readings averaged; (f) range of $V$V values appropriate to the component; (g) ensure self-heating is controlled by taking readings quickly (especially for the lamp and thermistor).

---

The Five Standard Components

OCR H556 requires you to know the characteristics of:

1. Ohmic (metallic) resistor at constant $T$T
2. Filament lamp
3. Semiconductor diode (including LED)
4. NTC thermistor
5. Light-dependent resistor (LDR)

We treat each in turn.

---

1. Ohmic Resistor — Straight Line Through Origin

The I-V characteristic of an ohmic conductor is a straight line through the origin, with the same slope in both positive and negative $V$V regions. The gradient is $1/R$1/R, and $R$R is constant (independent of $V$V).

Feature	Interpretation
Straight line	$I \propto V$I∝V — Ohm's law obeyed
Through origin	No offset; $I = 0$I=0 at $V = 0$V=0
Same gradient both sides	Symmetric — direction of current doesn't matter
Constant gradient	$R$R independent of $V$V

Physical explanation: at constant $T$T, the free-electron number density $n$n, carrier charge $q$q, drift velocity $v = eE\tau/m$v=eEτ/m, and cross-section $A$A are all constant. From $I = nAvq$I=nAvq and $E = V/L$E=V/L, $I \propto V$I∝V exactly — a straight line.

---

2. Filament Lamp — Lazy S Curve

The filament lamp's characteristic is S-shaped (also called a "lazy S" or "flattened S"). At very low voltages the filament is near room temperature, and the wire behaves almost ohmically — the I-V curve starts off as an approximately straight line near the origin. As $V$V increases, the filament heats up (a typical 12-V car headlamp filament reaches over 2500 °C), the ions of the tungsten lattice vibrate more violently, and electron scattering increases. The resistance rises.

So for the same $\Delta V$ΔV, you get a smaller $\Delta I$ΔI at higher voltages — the curve flattens. The symmetry point is the origin: reversing the current direction does not change the filament's physics, so the curve is rotationally symmetric about the origin (odd symmetry).

$V$V (V)	$I$I (A) (typical 12 V bulb)	$R = V/I$R=V/I ($\Omega$Ω)
0	0	—
1	0.45	2.2
3	0.95	3.2
6	1.35	4.4
9	1.65	5.5
12	1.90	6.3

The current roughly doubles between $0$0 and $1$1 V, but only increases by $\sim 40\%$∼40% from $6$6 to $12$12 V. The resistance has tripled across the same sweep.

Canonical OCR mark-scheme answer: "As $V$V (and hence $I$I) increases, $I^2 R$I2R power dissipation heats the filament. The lattice ions of the tungsten vibrate more vigorously, scattering electrons more frequently. The mean drift velocity falls (or: the mean free path shortens), so resistance $R = V/I$R=V/I rises. Therefore the I-V graph curves over — the same $\Delta V$ΔV gives a smaller $\Delta I$ΔI at higher voltages."

---

3. Semiconductor Diode — One-Way Valve

A diode is a non-linear, asymmetric device. It is designed to allow current to flow easily in one direction (forward bias) and almost not at all in the reverse direction (reverse bias) — until the reverse voltage exceeds a destructive breakdown threshold.

Features of the diode characteristic:

• Forward bias ($V > 0$V>0): almost no current flows until $V$V exceeds a turn-on voltage of about $0.6$0.6–$0.7$0.7 V (silicon p-n junction) or $0.3$0.3 V (germanium). LEDs turn on at $\sim 1.8$∼1.8–$3.4$3.4 V depending on colour. Beyond the turn-on voltage, the current rises exponentially with $V$V.
• Reverse bias ($V < 0$V<0): the current is nearly zero (a few $\mu$μA leakage) up to a breakdown voltage typically tens of volts negative, at which the diode (unless designed for it — Zener diodes are an exception) fails destructively.

Region	Approximate behaviour
$V < 0$V<0 (reverse)	$I \approx 0$I≈0 (tiny leakage, $\mu$μA)
$0 < V < 0.6$0<V<0.6	$I \approx 0$I≈0 (exponentially small)
$V > 0.6$V>0.6 (Si)	$I$I rises very rapidly (exponentially)

Physical mechanism: the diode is a p-n junction (p-doped silicon abutting n-doped silicon). At zero bias, an internal depletion region with built-in field forms. In reverse bias, the field widens and current is suppressed. In forward bias above $\sim 0.6$∼0.6 V, electrons can flood from the n-region into the p-region (and holes the other way), and the current rises exponentially with $V$V following the Shockley diode equation $I = I_0 (e^{eV/kT} - 1)$I=I0​(eeV/kT−1).

Because the turn-on voltage is set by the semiconductor band gap, LEDs made of different materials have different turn-on voltages:

LED colour	Approximate turn-on V	Photon energy (eV)
Red	1.8–2.0	1.9
Yellow / orange	2.0–2.2	2.1
Green	2.0–3.0	2.4
Blue	3.0–3.4	2.8
White (blue + phosphor)	3.0–3.4	(broad)

Higher-energy photons require a larger band gap, which in turn requires a larger applied voltage. The turn-on voltage is approximately equal to the band gap divided by $e$e.

---

4. NTC Thermistor — Self-Heating Curve

A thermistor is a resistor whose resistance depends strongly on temperature. The most common type at A-Level is NTC (negative temperature coefficient): its resistance decreases as temperature rises, because thermal excitation frees more charge carriers (increasing $n$n in lesson 2's $I = nAvq$I=nAvq).

If you draw an I-V characteristic for a thermistor in a circuit where power dissipation is significant, the curve is not a straight line — as $V$V increases, $I^2 R$I2R heating raises the thermistor's temperature, which lowers $R$R, which makes $I$I rise even more for the next $\Delta V$ΔV. The curve bends upwards (becomes progressively steeper).

Note the opposite curvature from the filament lamp: lamp curves down ($R$R rises with $T$T); thermistor curves up ($R$R falls with $T$T).

For small currents (or fast measurements) where the thermistor stays at room temperature, its I-V characteristic is essentially linear. For large currents where self-heating matters, the characteristic is markedly non-linear.

OCR mark-scheme phrasing: "As $T$T rises, more electrons gain enough thermal energy to become free charge carriers, so the number density $n$n rises (lesson 2). Since $I = nAvq$I=nAvq, at fixed $V$V the current $I$I rises, and so $R = V/I$R=V/I falls."

---

5. Light-Dependent Resistor (LDR)

The LDR is a resistor whose resistance depends on light intensity. In total darkness an LDR may have a resistance of several megohms; in bright sunlight it drops to a few hundred ohms — a change of $\sim 4$∼4 orders of magnitude.

The mechanism: photons knock electrons from the valence band into the conduction band, increasing the free-carrier density $n$n. Like the NTC thermistor, more carriers $\Rightarrow$⇒ lower resistance — but the controlling variable is illuminance, not temperature.

For a constant light level, the LDR's I-V characteristic is essentially linear (like an ohmic resistor) — it just has a different slope for each illumination level. It is the resistance that varies with light, not the linearity of the I-V curve at constant illumination.

Illumination	Typical resistance
Total darkness	1–10 M$\Omega$Ω
Indoor dim	10 k$\Omega$Ω
Indoor bright	1 k$\Omega$Ω
Direct sunlight	100–300 $\Omega$Ω

LDRs are widely used in light sensors for street lamps, burglar alarms, and automatic camera exposure systems.

---

Summary Table of I-V Characteristics

Component	Shape of I-V curve	Symmetric about origin?	$R$R constant?	Physical reason for shape
Ohmic resistor	Straight line through origin	Yes	Yes	Constant $n, A, v$n,A,v at fixed $T$T
Filament lamp	Lazy S curve (concave down)	Yes (rotationally)	No, $R$R rises with $V$V	Filament heats up; lattice scatters more
Diode / LED	Sharp knee at $0.6$0.6–$3$3 V; flat below	No (asymmetric)	No	Semiconductor band gap; one-way valve
NTC thermistor	Concave up (steepens)	Yes (rotationally)	No, $R$R falls with $T$T	Thermal excitation frees carriers
LDR (fixed light)	Straight line through origin	Yes	Yes, but depends on light	Photon excitation frees carriers

---

Decision Tree — Identifying a Component from its I-V Data

flowchart TD
  A["I-V data given"] --> B{"Symmetric about origin?"}
  B -->|No| C["DIODE / LED (flat below turn-on)"]
  B -->|Yes| D{"Straight line through origin?"}
  D -->|Yes| E["OHMIC resistor (or LDR at fixed light)"]
  D -->|"No, curves DOWN"| F["Filament lamp (R rises with V)"]
  D -->|"No, curves UP"| G["NTC thermistor (R falls with T)"]

This is the workflow for any "identify the component" exam question.

---

Worked Example 1 — Identifying a Component

An unknown component gives the following I-V data.

$V$V (V)	$I$I (mA)
$-1.0$−1.0	$-0.001$−0.001
$-0.5$−0.5	$-0.001$−0.001
$0$0	$0$0
$+0.4$+0.4	$+0.1$+0.1
$+0.6$+0.6	$+5.0$+5.0
$+0.7$+0.7	$+35$+35
$+0.8$+0.8	$+100$+100

Identify the component and explain.