Ch 8 · 4.3.3 Action and Use of Circuit Components · O Level Physics 5054

Topic 8 of 17 in Electricity and Magnetism — O Level Physics 5054 — 47 lessons.

Introduction

Street lamps switch on by themselves at dusk. A fire alarm sounds when a room gets too hot. Both use a sensor whose resistance changes, in a potential divider that turns that change into a change of voltage. (Syllabus section 4.3.3.)

Key ideas — Sensors whose resistance changes

NTC thermistor (negative temperature coefficient):

🧑‍🏫 Teacher's explanation

Imagine a water pipe where the width of the pipe changes depending on the environment. If the pipe gets wider when it gets hot, water flows through more easily. This is exactly how an NTC thermistor works: as the temperature goes up, the 'path' for electrons becomes wider (resistance decreases), allowing more current to flow.

📖 Definitions

🔍 Worked example — Easy

A circuit consists of a 12 V battery connected to a 2000Omega LDR and a 1000Omega fixed resistor in series. Calculate the voltage across the LDR when it is in a dark environment (resistance = 2000Omega).

🔍 Worked example — Exam-style

An LDR is used in a potential divider with a 5 V supply and a 10 kOmega fixed resistor. When light intensity increases, the LDR resistance decreases from 50 kOmega to 5 kOmega. Calculate the output voltage V_out across the LDR in bright light.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) Calculate the voltage across the LDR in the dark. [2] (b) Explain why the voltage across the LDR decreases when light shines on it. [2] [4 marks]

Key ideas — The potential divider

Two resistors in series across a supply share the supply p.d. between them. The larger resistor gets the larger share:

🧑‍🏫 Teacher's explanation

Imagine a water pipe with two different sized filters in a row. If you push water through both, the filter that is harder to push water through (higher resistance) will cause a bigger drop in water pressure (potential difference) across it. In a series circuit, the total voltage from the battery is 'split' between the components. The component with the higher resistance 'grabs' a larger share of the voltage.

📖 Definitions

🔍 Worked example — Easy

A 12 V battery is connected to two resistors in series, R_1 = 4 Omega and R_2 = 8 Omega. Calculate the potential difference across R_1.

🔍 Worked example — Standard

A potential divider uses a fixed resistor R_1 = 100 Omega and a variable resistor R_2. The supply voltage is 6 V. If the potential difference across R_1 is 2 V, find the resistance of R_2.

🔍 Worked example — Exam-style

In a circuit, a 10 V supply is connected to a thermistor and a fixed resistor in series. The thermistor's resistance decreases as temperature increases. If at 20 C the thermistor resistance is 500 Omega and the fixed resistor is 500 Omega, calculate the output voltage across the thermistor. Then, state what happens to this output voltage if the temperature increases.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — The variable potential divider

A variable potential divider (potentiometer) is a resistor with a sliding contact. The output p.d. is taken between one end and the slider. Moving the slider changes how the resistance is shared, so the output p.d. can be set to any value from zero up to the full supply p.d. (Used as a volume control or a dimmer.)

🧑‍🏫 Teacher's explanation

Imagine a long water pipe with a tap placed somewhere along its length. If you want to control how much water comes out of a side-pipe branching off the main line, you move the tap. If the tap is at the very beginning, no water flows into the side-pipe. If it is at the very end, all the water flows through. A variable potential divider works exactly like this, but with electricity instead of water.

📖 Definitions

🔍 Worked example — Easy

A 12 V battery is connected to a potential divider consisting of two resistors, R_1 = 40Omega and R_2 = 60Omega, in series. Calculate the potential difference across R_1.

🔍 Worked example — Standard

A variable resistor is used as a potential divider. The total supply voltage is 6.0 V. The slider is positioned such that the resistance of the bottom section (R_2) is 2.0 kOmega and the resistance of the top section (R_1) is 1.0 kOmega. Calculate the output voltage across R_2.

🔍 Worked example — Exam-style

In a circuit, a 10 V supply is connected to a potential divider. The output voltage V_out is 3.0 V. If the resistance of the resistor connected to the output is R_2 = 300Omega, calculate the resistance of the other resistor R_1.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Sensors in a potential divider

Put a thermistor or LDR in a potential divider with a fixed resistor. When its resistance changes, the share of the p.d. changes, and this output p.d. can switch on a lamp, buzzer or relay.

🧑‍🏫 Teacher's explanation

Imagine a potential divider as a tug-of-war between two resistors for the total voltage supplied by a battery. The total voltage is shared between them. If one resistor gets 'stronger' (higher resistance), it pulls more of the voltage to itself, leaving less for the other.

📖 Definitions

🔍 Worked example — Easy

A potential divider consists of a 10 kOmega fixed resistor and an LDR in series. The total voltage supplied is 6 V. When light shines on the LDR, its resistance is 2 kOmega. Calculate the potential difference across the LDR.

🔍 Worked example — Standard

A thermistor is used in a potential divider with a 4.0 kOmega fixed resistor. The input voltage is 12 V. When the temperature rises, the thermistor resistance drops to 1.0 kOmega. Calculate the voltage across the fixed resistor.

🔍 Worked example — Exam-style

In a street lamp circuit, an LDR and a 5.0 kOmega resistor are in series. The supply is 12 V. The lamp turns on when the voltage across the LDR reaches 9.0 V. Calculate the resistance of the LDR at the moment the lamp turns on.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) Explain why the voltage across the LDR decreases when light intensity increases. [2] (b) Calculate the resistance of the LDR when the voltage across it is 3.0 V. [2] [4 marks]

Worked example

Example 1. A 2.0 kΩ and a 4.0 kΩ resistor form a potential divider across a 9.0 V supply. Find the p.d. across each.

🔍 Worked example — Easy

A 12.0 V battery is connected across two resistors in series: R_1 = 400 Omega and R_2 = 800 Omega. Calculate the potential difference across the 800 Omega resistor.

🔍 Worked example — Standard

An LDR is used in a potential divider circuit with a 6.0 V supply and a 10 kOmega fixed resistor. In bright light, the LDR resistance is 2.0 kOmega. Calculate the voltage across the LDR in bright light.

⚠️ Common errors

Common mistakes

Practice

Answers: (1) It increases. (2) 60/90 × 12 = 8.0 V. (3) It increases: the thermistor's resistance falls, so it takes a smaller share of the supply p.d., and the fixed resistor takes a larger share. (4) To provide an output p.d. that can be varied smoothly from zero to the supply p.d., e.g. a volume control or a dimmer.

Ch 8 · 4.3.3 Action and Use of Circuit Components · O Level Physics 5054

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