CIE AS/A Level Physics 9.3 Resistance and resistivity Study Notes- 2025-2027 Syllabus
CIE AS/A Level Physics 9.3 Resistance and resistivity Study Notes – New Syllabus
CIE AS/A Level Physics 9.3 Resistance and resistivity Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on AS/A Level Physics latest syllabus with Candidates should be able to:
- define resistance
- recall and use V = IR
- sketch the I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp
- explain that the resistance of a filament lamp increases as current increases because its temperature increases
- state Ohm’s law
- recall and use R = ρL / A
- understand that the resistance of a light-dependent resistor (LDR) decreases as the light intensity increases
- understand that the resistance of a thermistor decreases as the temperature increases (it will be assumed that thermistors have a negative temperature coefficient
Definition of Resistance
The resistance of a component is a measure of how much it opposes the flow of electric current through it. It is defined as the ratio of potential difference across the component to the current flowing through it.
\( \mathrm{R = \dfrac{V}{I}} \)
Where:
- \( \mathrm{R} \): resistance (ohms, \( \mathrm{\Omega} \))
- \( \mathrm{V} \): potential difference across the component (volts, V)
- \( \mathrm{I} \): current through the component (amperes, A)
Explanation:
- A large resistance means a small current flows for a given potential difference.
- A small resistance means a large current flows for the same potential difference.
Resistance quantifies how difficult it is for charges to flow through a material or component. It depends on the material, temperature, and physical dimensions of the conductor.
Example
A potential difference of \( \mathrm{12 \ V} \) causes a current of \( \mathrm{3.0 \ A} \) in a resistor. Calculate its resistance.
▶️ Answer / Explanation
Using \( \mathrm{R = \dfrac{V}{I}} \):
\( \mathrm{R = \dfrac{12}{3.0} = 4.0 \ \Omega.} \)
Therefore, the resistance is \( \mathrm{4.0 \ \Omega.} \)
Example
If a resistor of \( \mathrm{6 \ \Omega} \) is connected to a \( \mathrm{9.0 \ V} \) battery, what is the current through it?
▶️ Answer / Explanation
Using \( \mathrm{I = \dfrac{V}{R}} \):
\( \mathrm{I = \dfrac{9.0}{6.0} = 1.5 \ A.} \)
Hence, the current through the resistor is \( \mathrm{1.5 \ A.} \)
Ohm’s Law — \( \mathrm{V = IR} \)
Statement: Ohm’s Law states that the current through a metallic conductor is directly proportional to the potential difference across it, provided the temperature and other physical conditions remain constant
\( \mathrm{V = IR} \)
Where:
- \( \mathrm{V} \) — potential difference (V)
- \( \mathrm{I} \) — current (A)
- \( \mathrm{R} \) — resistance (Ω)
Explanation:
- If the graph of \( \mathrm{V} \) versus \( \mathrm{I} \) is a straight line through the origin, the component obeys Ohm’s law and is called an ohmic conductor.
- The gradient of the \( \mathrm{V\text{-}I} \) graph gives the resistance.
For ohmic materials (like metallic resistors), resistance remains constant as long as temperature does not change.
Example
A 5 Ω resistor carries a current of 0.8 A. What is the potential difference across it?
▶️ Answer / Explanation
Using \( \mathrm{V = IR} \):
\( \mathrm{V = 0.8 \times 5 = 4.0 \ V.} \)
Hence, the potential difference across the resistor is 4.0 V.
Example
The current through a resistor is 2.5 A when a voltage of 10 V is applied. Find the resistance and verify if it obeys Ohm’s law when the voltage doubles.
▶️ Answer / Explanation
At 10 V: \( \mathrm{R = \dfrac{V}{I} = \dfrac{10}{2.5} = 4 \ \Omega.} \)
If voltage doubles to 20 V, current should also double to 5 A (since \( \mathrm{R} \) is constant).
The \( \mathrm{V\text{-}I} \) relationship remains linear — thus, the resistor obeys Ohm’s law.
I–V Characteristics of Different Components
The I–V characteristic of a component is a graph showing how the current (\( \mathrm{I} \)) varies with the applied potential difference (\( \mathrm{V} \)) across it. It provides insight into whether a component obeys Ohm’s law.
| Component | Graphical Description | Explanation |
|---|---|---|
| Metallic conductor (at constant temperature) |
Linear graph — straight line through the origin; current directly proportional to voltage. | Obeys Ohm’s law. Resistance remains constant because temperature is constant. Gradient \( = 1/R. \) |
| Filament lamp |
Curved graph — starts linear at low voltages, then flattens as voltage increases. | As current increases, the filament temperature rises, increasing resistance. Hence, current increases less rapidly with voltage. |
| Semiconductor diode |
Current almost zero for negative voltage (reverse bias); rapid rise after threshold (~0.6 V) in forward bias. | Non-ohmic component. Conducts in one direction only (forward bias). In reverse bias, current is negligible. |
Sketch Descriptions:
- Metallic conductor: Straight line through the origin (constant slope).
- Filament lamp: S-shaped curve — starts linear, then curves due to heating effects.
- Semiconductor diode: Very flat along negative side (almost zero current), then rises steeply on positive side after threshold.
The shape of the I–V graph reveals whether a component obeys Ohm’s law. Linear graphs indicate ohmic behaviour; nonlinear graphs indicate non-ohmic behaviour.
Example
Explain why the resistance of a filament lamp increases as current increases.
▶️ Answer / Explanation
As current increases, the filament’s temperature rises due to electrical heating. The increased temperature causes metal ions in the filament to vibrate more vigorously, impeding electron flow. Hence, resistance increases, and the I–V curve bends.
Example
Why does a diode conduct current in only one direction?
▶️ Answer / Explanation
In forward bias, the applied potential difference reduces the potential barrier at the p–n junction, allowing charge carriers to cross and current to flow. In reverse bias, the potential barrier increases, preventing current flow except for a negligible leakage current.
Hence, the diode allows current only in the forward direction.
Resistance of a Filament Lamp Increases with Current
In a filament lamp, as current increases, the wire filament (usually made of tungsten) becomes hotter due to electrical energy being converted to heat energy. This temperature rise causes the resistance of the filament to increase.
Reason:
- When the current flows, electrons collide with the lattice ions of the metal filament.
- As temperature increases, these ions vibrate more vigorously.
- This increases the frequency of collisions between electrons and ions, making it harder for electrons to move.
- Hence, resistance increases as current (and temperature) increases.
The resistance of a filament lamp is not constant; it increases with current because of the rise in temperature. Thus, it is a non-ohmic conductor.
Graphical Representation:
- The I–V graph of a filament lamp starts linear at low voltages (low temperatures).
- As current increases, the curve bends — showing that for larger voltages, the current increases more slowly.
Example
Why does a filament lamp not obey Ohm’s law even though it is made of metal?
▶️ Answer / Explanation
Although it is metallic, a filament lamp’s resistance changes as it heats up. Ohm’s law requires resistance to remain constant for a fixed temperature. Since the filament’s temperature increases with current, resistance increases, violating Ohm’s law.
Example
The resistance of a lamp at 2 V is 5 Ω, but at 6 V it is 8 Ω. Explain this change.
▶️ Answer / Explanation
At higher voltage, more current flows, causing the filament to heat up. The higher temperature increases atomic vibrations in the filament, which impede electron flow, increasing resistance from 5 Ω to 8 Ω.
Ohm’s Law
Statement: Ohm’s Law states that the current through a conductor is directly proportional to the potential difference across it, provided the physical conditions (particularly temperature) remain constant.
\( \mathrm{V \propto I} \quad \text{or} \quad \mathrm{V = IR} \)
Explanation:
- When the temperature of the conductor is constant, doubling the voltage doubles the current — the ratio \( \mathrm{V/I} \) remains constant.
- This constant of proportionality is the resistance (R).
Key Conditions for Ohm’s Law to Hold:
- Temperature must be constant.
- The material must be metallic or ohmic (linear \( \mathrm{V\text{-}I} \) relationship).
- No change in physical state (e.g., no heating or melting).
If the \( \mathrm{I\text{-}V} \) graph is a straight line through the origin, the component obeys Ohm’s law. Otherwise, it is a non-ohmic conductor (e.g., filament lamp, diode).
Example
A current of \( \mathrm{0.4 \ A} \) flows through a resistor when a \( \mathrm{2.0 \ V} \) potential difference is applied. Verify if the resistor obeys Ohm’s law when the potential difference is increased to \( \mathrm{4.0 \ V.} \)
▶️ Answer / Explanation
At 2 V: \( \mathrm{R = \dfrac{2.0}{0.4} = 5.0 \ \Omega.} \)
If Ohm’s law holds, at 4 V, \( \mathrm{I = \dfrac{V}{R} = \dfrac{4.0}{5.0} = 0.8 \ A.} \)
If current is measured as 0.8 A, the resistor obeys Ohm’s law (constant resistance). If not, it does not obey Ohm’s law.
Example
State one reason why a diode does not obey Ohm’s law.
▶️ Answer / Explanation
A diode conducts only after the forward voltage exceeds a threshold (about 0.6 V for silicon). The current–voltage relationship is nonlinear, so \( \mathrm{V/I} \) is not constant — hence, it does not obey Ohm’s law.
Relationship Between Resistance, Resistivity, Length, and Area
Formula:
\( \mathrm{R = \rho \dfrac{L}{A}} \)
Where:
- \( \mathrm{R} \): resistance (Ω)
- \( \mathrm{\rho} \): resistivity of the material (Ω·m)
- \( \mathrm{L} \): length of the conductor (m)
- \( \mathrm{A} \): cross-sectional area of the conductor (m²)
Explanation:
- Resistance increases with length (L): A longer conductor offers more opposition to current flow.
- Resistance decreases with cross-sectional area (A): A thicker conductor allows more charge to flow simultaneously.
- Resistivity (ρ): A material property that measures how strongly it resists current flow. It depends on the material and its temperature.
For a uniform conductor, resistance depends directly on its geometry and the material’s resistivity: long and thin wires have higher resistance than short and thick ones.
Example
A copper wire of length \( \mathrm{2.0 \ m} \) and cross-sectional area \( \mathrm{1.0 \times 10^{-6} \ m^2} \) has resistivity \( \mathrm{1.7 \times 10^{-8} \ \Omega m.} \) Calculate its resistance.
▶️ Answer / Explanation
Using \( \mathrm{R = \rho \dfrac{L}{A}} \):
\( \mathrm{R = \dfrac{1.7 \times 10^{-8} \times 2.0}{1.0 \times 10^{-6}} = 0.034 \ \Omega.} \)
Therefore, the resistance of the wire is \( \mathrm{0.034 \ \Omega.} \)
Example
The resistance of a copper wire is \( \mathrm{0.5 \ \Omega} \) when its length is \( \mathrm{2.0 \ m.} \) If the wire is stretched uniformly to double its original length, find the new resistance (assuming volume remains constant).
▶️ Answer / Explanation
For constant volume: \( \mathrm{A_1 L_1 = A_2 L_2 \Rightarrow A_2 = \dfrac{A_1 L_1}{L_2} = \dfrac{A_1}{2}.} \)
New resistance: \( \mathrm{R_2 = \rho \dfrac{L_2}{A_2} = \rho \dfrac{2L_1}{A_1/2} = 4 \rho \dfrac{L_1}{A_1} = 4R_1.} \)
Hence, \( \mathrm{R_2 = 4 \times 0.5 = 2.0 \ \Omega.} \)
Therefore, when the length is doubled, the resistance quadruples.
Resistance of a Light-Dependent Resistor (LDR)
A light-dependent resistor (LDR) is a semiconductor component whose resistance decreases as the light intensity incident on it increases.
Explanation:
- An LDR is made from a semiconductor material such as cadmium sulfide (CdS).
- When light shines on the LDR, the energy of the photons frees more electrons within the semiconductor.
- This increases the number of charge carriers (electrons), allowing more current to flow for the same potential difference.
- As a result, the resistance decreases with increasing light intensity.
Relationship:
As light intensity ↑ → number of charge carriers ↑ → resistance ↓
Graphical Representation:
- The graph of resistance (\( \mathrm{R} \)) versus light intensity is a downward curve — steep decrease at low light levels and gradually flattening at higher intensities.
Applications of LDRs:
- Automatic streetlights — turn on at night (high resistance in dark) and off during the day (low resistance in light).
- Camera exposure meters.
- Light-sensitive alarms and brightness sensors.
The resistance of an LDR decreases with increasing light intensity because more electrons are liberated by photons, increasing conductivity.
Example
Explain what happens to the resistance of an LDR when it is moved from a dark room into bright sunlight.
▶️ Answer / Explanation
In bright sunlight, more photons hit the LDR’s surface, releasing more free electrons. This increases the number of charge carriers, reducing the resistance of the LDR significantly. The current through the LDR therefore increases.
Example
In an automatic night lamp circuit, the lamp is connected in series with an LDR and a fixed resistor. Explain why the lamp switches on in darkness.
▶️ Answer / Explanation
In darkness, the LDR’s resistance becomes very high, increasing the potential difference across it. This triggers the lamp circuit to switch on. In bright light, the LDR’s resistance drops, reducing the voltage across the lamp, switching it off.
Resistance of a Thermistor (Negative Temperature Coefficient)
A thermistor is a temperature-sensitive resistor whose resistance changes with temperature. Most thermistors used in electronics have a negative temperature coefficient (NTC), meaning their resistance decreases as temperature increases.
Explanation:
- A thermistor is made of semiconductor material.
- As the temperature rises, thermal energy frees more electrons from their atoms within the semiconductor.
- The increased number of free charge carriers reduces the resistance, allowing current to flow more easily.
Relationship:
As temperature ↑ → charge carrier density ↑ → resistance ↓
Graphical Representation:
- The graph of resistance (\( \mathrm{R} \)) versus temperature (\( \mathrm{T} \)) is a downward curve — resistance falls rapidly at lower temperatures, then more gradually at higher temperatures.
Applications of Thermistors:
- Temperature sensors (e.g., thermostats, digital thermometers).
- Overcurrent protection (as resistance rises when overheated beyond limits).
- Car engine temperature monitoring.
- Battery temperature monitoring in mobile devices.
In an NTC thermistor, resistance decreases as temperature increases because higher thermal energy liberates more charge carriers, increasing conductivity.
Example
Explain why a thermistor’s resistance decreases when it is heated.
▶️ Answer / Explanation
Heating provides energy to free more electrons from atoms in the semiconductor. As the number of free charge carriers increases, the current can flow more easily, so resistance decreases.
Example
In a temperature control circuit, a thermistor is connected in series with a fan. Explain how the fan automatically turns on when the surroundings get hot.
▶️ Answer / Explanation
As temperature increases, the thermistor’s resistance decreases. This causes a higher current to flow through the circuit, increasing the voltage across the fan. When the voltage reaches a threshold, the fan turns on automatically, cooling the system.