Resistance and Resistivity

Overview

This lesson connects the circuit quantity resistance to the material property resistivity. You will use resistance in calculations, compare I-V graphs for common components, and explain how sensors such as LDRs and thermistors change resistance.

What You Need to Know

• Resistance is the ratio of potential difference to current for a component, so R = V / I.
• Use V = IR to calculate potential difference, current, or resistance.
• Ohm’s law states that current is directly proportional to potential difference for a metallic conductor at constant temperature.
• A metallic conductor at constant temperature has a straight-line I-V graph through the origin.
• A filament lamp becomes hotter as current increases, so its resistance increases and the I-V graph curves.
• A semiconductor diode conducts easily in one direction after its threshold p.d. but has very high resistance in the reverse direction.
• Resistivity depends on the material. Use R = rho L / A, where L is length and A is cross-sectional area.
• The resistance of an LDR decreases as light intensity increases. The resistance of a negative temperature coefficient thermistor decreases as temperature increases.

How to Work Through It

1. Start with V = IR calculations and make sure your units are volts, amperes, and ohms.
2. Compare I-V graphs for a resistor, filament lamp, and diode, linking each shape to changing resistance.
3. Use R = rho L / A to predict how changing length, area, or material affects resistance.
4. Apply sensor behaviour to explain how LDRs and thermistors can control voltage in later potential divider circuits.

Check Your Understanding

• What condition must be kept constant for a metallic conductor to obey Ohm’s law?
• Why does the I-V graph for a filament lamp become less steep as current increases?
• A wire is made twice as long with the same cross-sectional area. What happens to its resistance?
• How does the resistance of an LDR change when it is moved into brighter light?

Common Mistakes

• Treating resistance and resistivity as the same quantity.
• Sketching voltage-current graphs without checking which quantity is on each axis.
• Saying a filament lamp does not obey Ohm’s law without explaining the temperature change.
• Forgetting that a larger cross-sectional area gives a smaller resistance in R = rho L / A.

Next Steps

• Practise identifying components from I-V graphs and explaining the graph shape.
• Keep resistance, sensor, and energy ideas ready for the d.c. circuits topic.