Physics (9702) | Resistance and resistivity

Welcome to Resistance and Resistivity!

Hi there! This chapter is where we really start to understand the physics of electrical components. We've talked about current and voltage, but now we introduce the concept that dictates how much current can actually flow: Resistance.

Think of electricity as water flowing in a pipe. Voltage is the pressure pushing the water, and current is the flow rate. Resistance? Resistance is the roughness of the pipe walls that slows the flow down!

Understanding resistance and its intrinsic property, resistivity, is key to designing every electronic device, from your phone charger to giant transmission lines. Let's dive in!

Part 1: Defining Resistance and Ohm’s Law

1.1 What is Resistance? (9.3.1)

In simple terms, resistance is the opposition a material offers to the flow of electric current.

When electrons (charge carriers) move through a conductor, they collide with the fixed lattice ions (the atoms that make up the metal structure). These collisions transfer energy to the lattice ions, heating up the material, and slowing the electrons down. This “slowing down” is resistance.

Key Formula and Units (9.3.2)

Resistance (\(R\)) is defined using the relationship between potential difference (\(V\)) and current (\(I\)):

$$ R = \frac{V}{I} $$

The unit of resistance is the Ohm (\(\Omega\)). One ohm is defined as the resistance of a component when a potential difference of 1 Volt produces a current of 1 Ampere.

1.2 Stating Ohm’s Law (9.3.5)

Don't worry if this seems tricky at first—many students confuse the definition of resistance with Ohm's Law!

Ohm’s Law is a specific statement about certain materials (like most metals) under specific conditions:

Statement: For a metallic conductor at a constant temperature, the current flowing through it is directly proportional to the potential difference across it.

In mathematical terms, this means that \(V \propto I\), provided the temperature is constant. This also implies that for an ohmic conductor, the resistance \(R\) is constant.

Part 2: Current-Voltage (\(I-V\)) Characteristics

To understand if a component obeys Ohm's law, we plot a graph of current (\(I\)) against voltage (\(V\)) (or \(V\) against \(I\)). The shape of this graph tells us immediately if the resistance is constant or changing.

2.1 Ohmic Conductors (Metallic Wire) (9.3.3)

An ideal metallic conductor (like a copper wire) held at a constant temperature is Ohmic.

• Characteristic: The graph is a straight line passing through the origin.
• Interpretation: The gradient of the \(I-V\) graph is \(I/V = 1/R\). Since the line is straight, the gradient is constant, and therefore, R is constant.

2.2 Non-Ohmic Characteristics (9.3.3, 9.3.4)

Most components are Non-Ohmic, meaning their resistance changes depending on the applied voltage, usually because their temperature changes.

A. The Filament Lamp (Bulb)

When you sketch the \(I-V\) graph for a filament lamp, the curve bends towards the \(V\)-axis.

• Characteristic: The gradient decreases as \(V\) and \(I\) increase.
• Interpretation: Since the gradient (\(1/R\)) decreases, the Resistance (\(R\)) increases as the current increases.

Why does the resistance of a filament lamp increase? (9.3.4)

1. As current (\(I\)) increases, the power dissipated (\(P=I^2R\)) increases significantly.
2. This power causes the tungsten filament wire to heat up dramatically (it glows white-hot!).
3. As the temperature increases, the positive metal ions in the lattice vibrate with greater amplitude.
4. Electrons flowing through the wire collide more frequently with these vigorously vibrating ions.
5. These increased collisions lead directly to a higher opposition to current flow, meaning resistance increases.

B. Semiconductor Diode

A diode is designed to allow current flow easily in one direction (forward bias) and block it almost entirely in the other (reverse bias).

• Characteristic: The graph is flat near the origin and only increases sharply once a certain minimum forward voltage (around 0.6 V for silicon) is reached.
• Interpretation: In the forward direction, resistance starts very high, then drops dramatically. In the reverse direction, resistance is virtually infinite (until the component breaks down).

Key Takeaway: Ohmic materials have constant resistance (straight \(I-V\) line); non-Ohmic materials like lamps and diodes have resistance that varies, usually due to temperature changes.

Part 3: Resistance vs. Resistivity

We know that resistance is the total opposition, but if you take two pieces of the same copper wire, one long and thin, and one short and thick, will they have the same resistance? No! This is where we need the concept of resistivity.

3.1 Defining Resistivity (\(\rho\)) (9.3.6)

Resistivity (\(\rho\), the Greek letter rho) is an intrinsic property of a specific material, telling you how inherently difficult it is for charge to flow through it.

Analogy: If resistance is the total friction you feel riding a bike path, resistivity is the inherent roughness of the asphalt used to make the path.

The Resistivity Equation

The resistance \(R\) of a uniform conductor is determined by four factors:

1. The material (its resistivity, \(\rho\))
2. The length (\(L\))
3. The cross-sectional area (\(A\))
4. The temperature

The relationship derived from experiment is:

$$ R = \frac{\rho L}{A} $$

This means:

• Resistance is directly proportional to length (\(R \propto L\)). (A longer wire means more collisions.)
• Resistance is inversely proportional to cross-sectional area (\(R \propto 1/A\)). (A thicker wire provides more "paths" for the electrons, reducing overall opposition.)

Units of Resistivity

If we rearrange the formula to find \(\rho\):

$$ \rho = \frac{RA}{L} $$

The units for \(R\) are \(\Omega\), for \(A\) are \(\text{m}^2\), and for \(L\) are \(\text{m}\).

Therefore, the unit of resistivity (\(\rho\)) is Ohm-metre (\(\Omega\text{ m}\)).

Did you know? Conductors (like silver) have very low resistivity (around \(10^{-8} \Omega\text{ m}\)), while insulators (like rubber) have extremely high resistivity (around \(10^{15} \Omega\text{ m}\)). This vast difference is what makes modern electronics possible!

Key Takeaway: Resistivity defines the material's innate ability to conduct, independent of its shape, while Resistance is the measurable opposition for a specific object.

Part 4: Variable Resistors – Sensors and Control

Some electronic components are specifically designed so that their resistance changes significantly when external physical conditions change. These are crucial for building sensors and control circuits.

4.1 Light-Dependent Resistors (LDRs) (9.3.7)

An LDR is a semiconductor device whose resistance depends on the intensity of light falling on it.

The Rule: The resistance of an LDR decreases as the light intensity increases.

(Less light $\rightarrow$ High R; More light $\rightarrow$ Low R)

How it works: Light energy frees charge carriers (electrons) in the semiconductor material. More free carriers mean more ways for current to flow, hence less resistance.

Real-World Example: LDRs are commonly used in automatic streetlights. When the sun sets (light intensity decreases), the LDR resistance increases, triggering a circuit that switches the light on.

4.2 Thermistors (NTC) (9.3.8)

A thermistor is a resistor whose resistance varies significantly with temperature. The type studied in the AS syllabus is the Negative Temperature Coefficient (NTC) thermistor.

The Rule: The resistance of an NTC thermistor decreases as the temperature increases.

(Low temperature $\rightarrow$ High R; High temperature $\rightarrow$ Low R)

How it works: Like the LDR, the heat energy (high temperature) provides enough energy to liberate more charge carriers within the semiconductor structure, increasing conductivity and reducing resistance.

Real-World Example: Thermistors are used in temperature probes (like in medical thermometers or car engines) and thermostats. If a system gets too hot, the thermistor's resistance drops, which can trigger a cooling fan or shutdown mechanism.