Grade 10 Physical Sciences · Electricity and Magnetism

Use series and parallel circuit rules

Use how current and voltage behave in series and parallel circuits to find meter readings (current is the same everywhere in a series circuit).

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Question 8.5 · May/June 2025 · Paper 1 · National (DBE) · 3 marks

In the circuit diagram below, the battery has an emf of

24

V and an internal resistance of

0, 3 Ω

. Light bulb L has a resistance of

9, 5 Ω

and R is a resistor of unknown resistance. Ignore the resistance of the ammeters and the connecting wires. Diagram for this question

The letters A to F represent different quantities in the circuit, as shown in the table below.

Switch

S_{1}

is now OPENED, while switch

S_{2}

is CLOSED. Diagram

8.5 Write down the LETTERS of the quantities that will now be equal to zero.(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: use series and parallel circuit rules

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3. Question 1.8 · November 2023 · Paper 1 · National (DBE) · 2 marks
Various options are provided as possible answers to the following questions. Each question has only ONE correct answer.
1.8 Four voltmeters, V $_{1}$ , V $_{2}$ , V $_{3}$ and V $_{4}$ , are connected in a circuit, as shown in the diagram below.

Which voltmeter(s) will have the same reading as voltmeter V $_{1}$ when the switch is open?(2)
1. A V $_{2}$ only
2. B V $_{3}$ only
3. C V $_{4}$ only
4. D V $_{2}$ and V $_{4}$
Show the memo (1 tick)Memo
1. ✓
  Correct optionWith the switch open no current flows. V $_{1}$ reads the emf. There is no potential drop across R or the ammeter ( $V = I R = 0$ ), so V $_{2}$ and V $_{4}$ read zero. The whole emf appears across the open switch, so V $_{3}$ reads the same as V $_{1}$ .
  
  Answer: B
  2 marks · Use series and parallel circuit rules
4. Question 1.8 · November 2022 · Paper 1 · National (DBE) · 2 marks
Various options are provided as possible answers to the following questions. Each question has only ONE correct answer.
1.8 The emf of a battery is $ε$ and its internal resistance is $r$ . The battery is connected to three resistors and four voltmeters, as shown below. The resistance of the conducting wires is negligible, while the voltmeters have very high resistances.

Which ONE of the following equations represents the reading on voltmeter $V_{1}$ in terms of the readings on the other voltmeters?(2)
1. A $V_{1} = V_{2} + V_{3}$
2. B $V_{1} = V_{2} + \frac{1}{2} V_{3}$
3. C $V_{1} = V_{2} + V_{3} + V_{4}$
4. D $V_{1} = V_{2} + 2 V_{3}$
Show the memo (1 tick)Memo
1. ✓
  Voltage in series and parallel $V_{1}$ measures the potential difference across the battery terminals, i.e. across the whole external circuit.
  $R_{2}$ and $R_{3}$ are in parallel, so $V_{3} = V_{4}$ (the potential difference across the parallel combination).
  $R_{1}$ is in series with the parallel combination, so $V_{1} = V_{2} + V_{3}$ .
  
  Answer: A
  2 marks · Use series and parallel circuit rules
5. Question 8.2.2 · November 2024 · Paper 1 · National (DBE) · 3 marks
$L_{1}$ and $L_{2}$ are two light bulbs that have the following ratings:

$L_{1}$ : $36$ W ; $20$ V and $L_{2}$ : $48$ W ; $32$ V

The two bulbs are connected as shown in the circuit diagram below. The battery has an internal resistance of $0, 6 Ω$ while the conducting wires and the ammeters have negligible resistance. $R_{1}$ and $R_{2}$ are resistors.
8.2 If both light bulbs operate as RATED, calculate the:
8.2.2 Reading on ammeter $A_{1}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Current in $L_{1}$ For $L_{1}$ : $P = V I$
  $36 = 20 I$
  $I = 1, 8$ A
  1 mark · Calculate electrical power and energy
2. ✓
  Add the branch currents $I_{TOT} = 1, 5 + 1, 8$
  1 mark · Use series and parallel circuit rules
3. ✓
  Answer $= 3, 3$ A
  1 mark · Use series and parallel circuit rules
6. Question 8.2.2 · May/June 2023 · Paper 1 · National (DBE) · 4 marks
A battery with unknown emf ( $ε$ ) and unknown internal resistance (r) is connected to three resistors, a high-resistance voltmeter, two switches and two ammeters of negligible resistance, as shown below.
8.2 Both switch S $_{1}$ and switch S $_{2}$ are CLOSED. The reading on ammeter A $_{1}$ is $1, 5$ A.

Calculate the:
8.2.2 Reading on ammeter A $_{2}$ (4)
Show the memo (4 ticks)Memo
1. ✓
  METHOD 1: Formula $R = \frac{V}{I _{3}}$
  1 mark · Apply Ohm's law
2. ✓
  METHOD 1: Substitution $3 = \frac{10 , 5}{I _{3}}$
  $I_{3} = 3, 5$ A
  1 mark · Apply Ohm's law
3. ✓
  METHOD 1: Addition of currents $I_{T} = 1, 5 + 3, 5$
  1 mark · Use series and parallel circuit rules
4. ✓
  METHOD 1: Answer with unit $I_{T} = 5$ A
  1 mark · Use series and parallel circuit rules

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