# I-V Characteristics

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u9-i-v-characteristics/

This sub-topic explores how current ($I$) changes with applied potential difference ($V$) for common electrical components, distinguishes ohmic vs non-ohmic behaviour, and links graph shape to underlying physical properties like resistance and temperature.

**Prerequisites:** [Ohm's law and resistance definition](https://www.owlsprep.com/study/cie-9702-u9-ohm-s-law-resistance/)

## Learning objectives

- Interpret I-V and V-I graphs for different electrical components
- Distinguish between ohmic and non-ohmic conductors
- Link I-V curve shape to physical properties like resistance and temperature
- Sketch I-V characteristics for common CIE A-Level components

## I-V Characteristics and Ohmic Conductors

**I-V Characteristic** — A graph plotting current flowing through a component against the potential difference applied across it, measured at constant physical conditions

*Example:* A straight line through the origin for an ohmic resistor at constant temperature

An ohmic conductor follows Ohm's law when physical conditions (most importantly temperature) are held constant. For ohmic conductors, current is directly proportional to potential difference, so resistance is always constant.

$$I \propto V \implies R = \frac{V}{I} = \text{constant}$$

**Worked example:** A 10 Ω ohmic resistor has 5.0 V applied across it. Describe its I-V characteristic and calculate the current at 5.0 V.

1. 1. For an ohmic resistor, the I-V characteristic is a straight line passing through the origin, with gradient equal to $\frac{1}{R}$.
2. 2. Use Ohm's law to calculate current at 5.0 V:
3. $$I = \frac{V}{R} = \frac{5.0}{10} = 0.5 \text{ A}$$
4. 3. The line extends linearly into the negative quadrant: reversing the potential difference reverses current proportionally, so resistance remains constant.

## Non-ohmic Behaviour: Filament Lamp

**Non-ohmic Conductor** — A conductor that does not follow Ohm's law: current is not directly proportional to potential difference, so resistance changes with applied voltage

*Example:* Filament lamp, semiconductor diode

A filament lamp contains a thin tungsten metal filament. As potential difference increases, current increases, which increases power dissipation and raises the filament temperature. For metals, resistance increases with temperature because increased lattice vibration causes more frequent scattering of free electrons, reducing drift speed.

Since gradient of the I-V graph is $\frac{1}{R}$, increasing resistance makes the gradient decrease as V increases, so the graph curves away from the current axis.

**Worked example:** Explain why the I-V characteristic of a filament lamp curves away from the current axis at high potential differences.

1. 1. Higher potential difference leads to higher current, which increases power dissipation in the filament.
2. 2. Increased power raises the temperature of the tungsten filament.
3. 3. For metals, resistance increases with temperature due to more frequent collisions between free electrons and lattice ions.
4. 4. Since $I = \frac{V}{R}$, a larger increase in R for a given increase in V leads to a smaller increase in I, so the graph curves away from the I axis.

> **Exam tip:** Always link the shape of the I-V curve to changes in resistance and the underlying physical cause (usually temperature change) in CIE written exams.

## Non-ohmic Behaviour: Semiconductor Diode

A diode is a semiconductor component that only conducts current when it is forward biased (potential difference applied in the correct direction). It has very high resistance in reverse bias, so almost no current flows until breakdown.

For a silicon diode, current remains negligible in forward bias until the potential difference exceeds the threshold voltage (~0.6 V). Above this voltage, resistance drops rapidly and current increases very sharply.

**Worked example:** Describe the I-V characteristic of a silicon diode and explain its shape.

1. 1. For negative (reverse bias) potential difference, draw a line almost along the x-axis with negligible current, as resistance is extremely high.
2. 2. For positive (forward bias) potential difference between 0 and ~0.6 V, current still remains almost zero.
3. 3. Above 0.6 V (threshold voltage), draw a steep upward curve: current increases sharply with voltage because resistance drops rapidly once the junction is activated.
4. 4. The shape arises because the diode junction requires a minimum voltage to mobilize charge carriers for conduction.

## Other Common Components: Thermistor and LDR

CIE exams regularly test I-V characteristics for two additional common sensors:

- **NTC Thermistor**: Resistance decreases as temperature increases. At constant temperature, it is ohmic, so I-V is a straight line.
- **Light-Dependent Resistor (LDR)**: Resistance decreases as light intensity increases. At constant light intensity, it is ohmic, so I-V is a straight line.

**Worked example:** How does the I-V characteristic of an NTC thermistor change when temperature increases from 20°C to 50°C?

1. 1. Resistance is defined as $R = \frac{V}{I} = \frac{1}{\text{gradient of I-V graph}}$ at any point.
2. 2. For an NTC thermistor, increasing temperature decreases resistance, so gradient of the I-V graph increases.
3. 3. The I-V characteristic remains a straight line through the origin (it is still ohmic at constant temperature) but becomes steeper at higher temperatures.

## Common pitfalls

- **Wrong:** Claiming gradient of an I-V graph equals resistance
  - Why it fails: Most students mix up the relationship between gradient and resistance for I-V plots
  - Correct: Always remember $R = \frac{V}{I}$, so resistance is V divided by I at a point, which equals the reciprocal of the gradient of the I-V graph.
- **Wrong:** Drawing significant current for a diode in reverse bias before breakdown
  - Why it fails: Markers penalize incorrect shape that does not match standard diode behaviour
  - Correct: Draw the reverse bias part of the diode I-V curve almost along the x-axis, with negligible current until breakdown voltage.
- **Wrong:** Forgetting to extend ohmic resistor I-V characteristics to the negative quadrant
  - Why it fails: Reversing voltage reverses current proportionally, so the line should cover all quadrants
  - Correct: Always extend the straight line for an ohmic conductor into the negative V/negative I quadrant when asked for a full characteristic.
- **Wrong:** Stating filament lamps are non-ohmic just because resistance changes with temperature
  - Why it fails: Non-ohmic means resistance changes with applied voltage/current, not just with temperature itself
  - Correct: State that changing applied V changes current, which changes temperature, which changes R, so V is not proportional to I, hence it is non-ohmic.
- **Wrong:** Assuming all thermistors have increasing resistance with temperature
  - Why it fails: CIE almost exclusively tests negative temperature coefficient (NTC) thermistors
  - Correct: Assume NTC thermistors (resistance decreases with increasing temperature) unless the question explicitly states it is a PTC thermistor.

## Cheatsheet

| Component | Ohmic/Non-ohmic | I-V Graph Shape | Key Property |
| --- | --- | --- | --- |
| Ohmic Resistor | Ohmic | Straight line through origin | R = constant at constant T |
| Filament Lamp | Non-ohmic | Curve bending away from I axis | R increases as V increases (higher T) |
| Silicon Diode | Non-ohmic | ~Zero I < 0.6 V forward, steep I after; ~Zero I reverse | Conducts only above forward threshold voltage |
| NTC Thermistor (constant T) | Ohmic | Straight line through origin | Steeper gradient (lower R) at higher T |
| LDR (constant light) | Ohmic | Straight line through origin | Steeper gradient (lower R) at higher light intensity |

## What's next

Understanding I-V characteristics is foundational for all further topics in electricity, from circuit analysis to semiconductor devices and practical exam questions. The concepts of resistance change with temperature and light underpin most common sensor circuits, which appear regularly in both multiple-choice and written papers. This topic also connects directly to practical assessment, where you may be asked to plan an experiment to measure I-V characteristics of components, a common long question in Paper 3. Mastering this sub-topic makes all subsequent electricity topics much easier to understand.

- [Temperature dependence of resistance](https://www.owlsprep.com/study/cie-9702-u9-temperature-dependence-of-resistance/)
- [D.C. circuits](https://www.owlsprep.com/study/cie-9702-u10-overview/)
- [Circuit symbols and diagrams](https://www.owlsprep.com/study/cie-9702-u10-circuit-symbols-and-diagrams/)

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