📘 Chapter 36 : V-I Characteristics (Linear and Non-Linear) (Class XII)
🔷 1. Introduction
After understanding Ohm's Law, it is important to study how electric current changes with the applied potential difference. This relationship between voltage and current is represented graphically by a V-I Characteristic Curve.
The shape of the V-I graph helps us determine whether a conductor obeys Ohm's Law or not. Based on the graph, electrical devices are classified into Linear (Ohmic) and Non-Linear (Non-Ohmic) devices.
🔷 2. What is a V-I Characteristic?
Ethan: Professor, what do we mean by the V-I characteristic of a conductor?
Professor: The V-I characteristic is a graph showing how the electric current flowing through a conductor changes as the applied potential difference changes.
Academic Definition
The V-I characteristic is the graphical relationship between the potential difference (V) applied across a conductor and the current (I) flowing through it.
🔷 3. Why is the V-I Graph Important?
Ethan: Professor, why do we study this graph?
Professor: The V-I graph tells us how a material behaves electrically. It helps us determine whether the resistance remains constant or changes with voltage or current.
- It verifies Ohm's Law.
- It helps identify ohmic and non-ohmic devices.
- It is used to study electrical components and materials.
- It provides information about resistance.
🔷 4. Linear (Ohmic) V-I Characteristics
Ethan: Professor, what is a linear V-I characteristic?
Professor: A conductor has a linear V-I characteristic when the current increases proportionally with the applied voltage.
This means,
V ∝ I
or,
V = IR
Since the ratio V/I remains constant, the resistance remains constant.
Characteristics of Linear Conductors
- Obey Ohm's Law.
- Resistance remains constant.
- V-I graph is a straight line.
- The graph passes through the origin.
- Current is directly proportional to voltage.
🔷 5. Physical Meaning of a Linear Graph
Ethan: Professor, what does a straight-line graph tell us physically?
Professor: A straight-line graph means that every time the voltage is doubled, the current also doubles. Similarly, if the voltage becomes three times larger, the current also becomes three times larger.
Therefore, the conductor offers the same resistance throughout the experiment.
🔷 6. Non-Linear (Non-Ohmic) V-I Characteristics
Ethan: Professor, what is a non-linear V-I characteristic?
Professor: In some electrical devices, the current is not directly proportional to the applied voltage. Therefore, the V-I graph becomes curved instead of straight.
In such devices,
V is not proportional to I
Hence, the resistance continuously changes with voltage or current.
Characteristics of Non-Linear Conductors
- Do not obey Ohm's Law.
- Resistance is not constant.
- V-I graph is curved.
- Current is not directly proportional to voltage.
- The slope changes from point to point.
🔷 7. Why Do Non-Linear Characteristics Occur?
Ethan: Professor, why do some devices show curved graphs?
Professor: Because their resistance changes during operation.
This may happen due to:
- Increase in temperature.
- Semiconductor properties.
- Material composition.
- Change in carrier concentration.
- Internal electronic processes.
🔷 8. Examples
| Linear (Ohmic) | Non-Linear (Non-Ohmic) |
|---|---|
| Copper wire | PN Junction Diode |
| Aluminium wire | LED |
| Silver wire | Thermistor |
| Metallic resistor | Filament lamp |
🔷 9. Comparison Between Linear and Non-Linear Characteristics
| Linear (Ohmic) | Non-Linear (Non-Ohmic) |
|---|---|
| Straight-line graph. | Curved graph. |
| Resistance remains constant. | Resistance changes continuously. |
| Obeys Ohm's Law. | Does not obey Ohm's Law. |
| Constant slope. | Variable slope. |
| Current is proportional to voltage. | Current is not proportional to voltage. |
📦 10. Important Results (Must Remember)
- V-I characteristics represent the relationship between voltage and current.
- Linear conductors obey Ohm's Law.
- Non-linear conductors do not obey Ohm's Law.
- Linear graphs are straight lines passing through the origin.
- Non-linear graphs are curved.
- Constant resistance produces a linear graph.
- Variable resistance produces a non-linear graph.
- The slope of the V-I graph provides information about resistance.
🧠 11. Conceptual Questions
🔹 Q1
Ethan: What is meant by a V-I characteristic?
Professor: It is the graph showing the relationship between voltage and current for an electrical device.
🔹 Q2
Ethan: Which conductors have a straight-line V-I graph?
Professor: Ohmic or linear conductors.
🔹 Q3
Ethan: Why is the graph of a diode curved?
Professor: Because its resistance changes with the applied voltage, so it does not obey Ohm's Law.
🔹 Q4
Ethan: What does the slope of a V-I graph indicate?
Professor: It provides information about the electrical resistance of the device.
🔹 Q5
Ethan: Can a filament lamp be considered an ohmic conductor?
Professor: No. As the filament heats up, its resistance changes, giving a non-linear V-I characteristic.
🔷 12. Applications
- Testing electrical components.
- Designing electronic circuits.
- Selection of resistors and semiconductors.
- Analysis of diodes and LEDs.
- Material characterization in electrical engineering.
🔷 13. Summary
The V-I characteristic graph describes how electric current varies with the applied potential difference. Linear (ohmic) conductors exhibit a straight-line graph because their resistance remains constant and they obey Ohm's Law. Non-linear (non-ohmic) devices show curved graphs because their resistance changes with voltage, current, or temperature. Studying V-I characteristics is essential for understanding the electrical behavior of different materials and devices.
✨ End of Topic: V-I Characteristics (Linear and Non-Linear) ✨
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