Ch 5 · 4.2.4 Resistance · O Level Physics 5054

Topic 5 of 17 in Electricity and Magnetism — O Level Physics 5054 — 60 lessons.

Introduction

The same battery pushes a large current through a short, thick copper wire but only a small current through a lamp filament. The difference is resistance: how much a component opposes the flow of current. (Syllabus section 4.2.4.)

Key ideas — Resistance

R = V/I

🧑‍🏫 Teacher's explanation

Think of electricity like water flowing through a pipe. The current is the flow rate of the water, and the potential difference (voltage) is the water pressure pushing it through. Resistance is like the narrowness or the roughness of the pipe. If the pipe is very narrow (small cross-sectional area) or very long, it is much harder for the water to get through, meaning the resistance is high.

📖 Definitions

🔍 Worked example — Easy

A component has a potential difference of 4.5 V across it and a current of 0.5 A flowing through it. Calculate the resistance.

🔍 Worked example — Standard

A wire has a resistance of 2.0 Omega. If the length of the wire is doubled while the cross-sectional area remains the same, what is the new resistance?

🔍 Worked example — Exam-style

A filament lamp is connected to a 12 V supply. Initially, the current is 1.2 A. As the lamp glows brighter, the temperature increases and the resistance rises to 1.5 Omega. Calculate the new current flowing through the lamp.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) State the formula used to calculate the resistance R. [1] (b) Describe how the student could use a voltmeter and an ammeter to determine the resistance of a single component. [3] (c) If the wire is stretched so that it becomes thinner, state and explain the effect on its resistance. [2] [6 marks]

Key ideas — Resistance of a wire

For a wire of a given material (at constant temperature):

🧑‍🏫 Teacher's explanation

Think of electricity flowing through a wire like water flowing through a pipe. If the pipe is very long, the water has to fight through more friction against the walls, making it harder to flow (higher resistance). If the pipe is very wide, the water flows much more easily because there is more space to move (lower resistance).

📖 Definitions

🔍 Worked example — Easy

A wire has a resistance of 2.5 Omega. Calculate the resistance if the length of the wire is doubled while the cross-sectional area remains the same.

🔍 Worked example — Standard

A wire with resistance R has a cross-sectional area A. If the area is reduced to 1/3 of its original value, what is the new resistance in terms of R?

🔍 Worked example — Exam-style

A constant temperature resistor has a voltage of 6.0 V across it and a current of 0.50 A flowing through it. Calculate the resistance.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Ohm's law

Ohm's law: the current through a metallic conductor is directly proportional to the p.d. across it, provided the temperature stays constant.

🧑‍🏫 Teacher's explanation

Imagine water flowing through a pipe. The pressure pushing the water (voltage) determines how fast it flows (current). If the pipe gets narrower (smaller cross-sectional area), it becomes harder for water to pass through, increasing the resistance. If the pipe gets longer, the water has more distance to travel against friction, also increasing resistance.

📖 Definitions

🔍 Worked example — Easy

A fixed resistor has a potential difference of 6.0 V across it when a current of 0.50 A flows through it. Calculate the resistance.

🔍 Worked example — Standard

A wire has a resistance of 4.0 Omega. If the length of the wire is doubled while the cross-sectional area remains the same, what is the new resistance?

🔍 Worked example — Exam-style

A wire with resistance R has a cross-sectional area A. If the area is halved (A/2) and the length is doubled (2L), calculate the new resistance in terms of R.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Current–voltage (I–V) graphs

(a) Resistor of constant resistance (ohmic conductor). A straight line through the origin. Current is proportional to p.d.; resistance is constant. Reversing the p.d. gives the same line continuing into the negative quarter.

🧑‍🏫 Teacher's explanation

Imagine water flowing through a pipe. A standard resistor is like a pipe of constant width; if you increase the water pressure (voltage), the flow rate (current) increases at a steady, predictable rate. This is a straight line on a graph.

📖 Definitions

🔍 Worked example — Easy

A resistor has a potential difference of 1.5 V across it when a current of 0.5 A flows through it. Calculate the resistance.

🔍 Worked example — Standard

A filament lamp is connected to a 6.0 V supply. At 3.0 V, the current is 0.4 A. At 6.0 V, the current is 0.6 A. Calculate the resistance at 6.0 V.

🔍 Worked example — Exam-style

A wire has a resistance of 4.0 Omega. If the wire is stretched to double its length while keeping its volume constant, what is the new resistance? (Assume resistance is directly proportional to length and inversely proportional to cross-sectional area).

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) Describe how the student should set up the circuit to measure the resistance of the wire. [3] (b) The student plots a graph of current (I) against potential difference (V). The graph is a straight line passing through the origin. What does this tell the student about the wire? [1] [4 marks]

Key ideas — Temperature and resistance

For a metal resistor such as a lamp filament, resistance increases as temperature increases. The metal ions vibrate more strongly, so the free electrons collide with them more often and their flow is impeded more.

🧑‍🏫 Teacher's explanation

Imagine a crowded hallway in a school. If everyone is walking calmly, people can move through easily. But if everyone starts dancing wildly and jumping around (like vibrating ions in a hot wire), they will constantly bump into the people trying to walk through (the electrons). This makes it much harder for the crowd to move from one end to the other. In physics, we call this 'resistance'.

📖 Definitions

🔍 Worked example — Easy

A resistor has a potential difference of 4.5 V across it when a current of 0.50 A flows through it. Calculate the resistance.

🔍 Worked example — Standard

A wire has a resistance of 2.0 Omega. If the length of the wire is doubled while the cross-sectional area remains the same, what is the new resistance?

🔍 Worked example — Exam-style

A filament lamp is connected to a 12 V supply. Initially, the current is 1.2 A. As the lamp warms up, the resistance increases to 15 Omega. Calculate the new current flowing through the lamp.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Practical notes

To investigate a wire's length, connect different lengths of the same wire (measured with a metre rule) using crocodile clips, and find R for each: R is proportional to length.

Worked example

Example 1. A p.d. of 12 V drives a current of 0.50 A through a resistor. Find its resistance.

🔍 Worked example — Easy

A potential difference of 12 V is applied across a resistor, resulting in a current of 0.50 A. Calculate the resistance of the resistor.

🔍 Worked example — Standard

A wire of length 2.0 m has a resistance of 6.0Omega. Calculate the resistance of a wire of the same material that is 5.0 m long.

🔍 Worked example — Exam-style

A wire has a resistance of 12 Omega. If the cross-sectional area is doubled while the length remains the same, what is the new resistance?

⚠️ Common errors

Common mistakes

Practice

Answers: (1) V = IR = 0.20 × 30 = 6.0 V. (2) The current through a metallic conductor is directly proportional to the p.d. across it, provided the temperature remains constant. (3) A curve through the origin that gets flatter as the p.d. increases; as current increases, the filament gets hotter, so its resistance increases. (4) 12 Ω. (5) It allows current to flow in one direction only (very high resistance in the reverse direction).

Ch 5 · 4.2.4 Resistance · O Level Physics 5054

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