Grade 10 Physical Sciences · Electricity and Magnetism

Calculate equivalent resistance

Calculate the total resistance of resistors in series (R = R₁ + R₂) or parallel (1/R = 1/R₁ + 1/R₂), for example two 4 Ω in parallel give 2 Ω.

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Question 8.2 · May/June 2024 · Paper 1 · National (DBE) · 5 marks

A battery of emf

12

V and internal resistance

0, 2 Ω

is connected to three resistors, a high-resistance voltmeter and two switches, an ammeter and connecting wires of negligible resistance, as shown in the circuit diagram below. The three resistors have different and unknown resistances.

The resistance of

R_{Y}

is TWICE the resistance of

R_{X}

.

When both switches are CLOSED, the reading on the ammeter is

5, 5

8.2 Calculate the resistance of resistor

R_{Y}

.(5)

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

More past paper questions: calculate equivalent resistance

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3. Question 8.2.1 · November 2022 · Paper 1 · National (DBE) · 4 marks
The circuit diagram below shows four resistors connected to a battery of emf $ε$ and internal resistance $r$ . The resistances of the ammeter and the connecting wires are negligible, while the voltmeters have very high resistances.
8.2 Switch S is CLOSED.

The reading on the ammeter is $3, 5$ A.
8.2.1 Calculate the total external resistance of the circuit.(4)
Show the memo (4 ticks)Memo
1. ✓
  Parallel formula $\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}}$ (OR $R_{p} = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$ )
  1 mark · Calculate equivalent resistance
2. ✓
  Substitution $\frac{1}{R _{p}} = \frac{1}{1} + \frac{1}{5}$
  $R_{p} = 0, 83 Ω$
  1 mark · Calculate equivalent resistance
3. ✓
  Adding the $4 Ω$ $R_{T} = 0, 83 + 4$
  1 mark · Calculate equivalent resistance
4. ✓
  Answer $R_{T} = 4, 83 Ω$
  1 mark · Calculate equivalent resistance
4. Question 8.3.1 · May/June 2022 · Paper 1 · National (DBE) · 5 marks
In the circuit below a battery of UNKNOWN emf and an internal resistance of $0, 5 Ω$ is connected to two resistors of $4 Ω$ and $8 Ω$ each, and a resistor R of unknown resistance.

Ignore the resistance of the connecting wires.
8.3 When switch S is CLOSED, voltmeter V $_{2}$ reads $8, 8$ V.
8.3.1 Calculate the resistance of resistor R.(5)
Show the memo (5 ticks)Memo
1. ✓
  Current from the lost volts $V_{in t} = 10 - 8, 8 = 1, 2$ V
  $V_{in t} = I r$
  $1, 2 = I (0, 5)$
  $I = 2, 4$ A
  1 mark · Use emf and internal resistance
2. ✓
  Substitution of V $R_{e x t} = \frac{V}{I} = \frac{8 , 8}{\dots}$
  1 mark · Apply Ohm's law
3. ✓
  Substitution of I $R_{e x t} = \frac{8 , 8}{2 , 4} = 3, 67 Ω$ ( $3, 667$ )
  1 mark · Apply Ohm's law
4. ✓
  Parallel combination $R_{P} = \frac{12 R}{12 + R}$
  $3, 67 = \frac{12 R}{12 + R}$
  
  OR
  
  $\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}}$ : $\frac{1}{3 , 67} = \frac{1}{R} + \frac{1}{12}$
  1 mark · Calculate equivalent resistance
5. ✓
  Answer with unit $R = 5, 29 Ω$ ( $5, 28$ )
  1 mark · Calculate equivalent resistance
5. Question 7.3.1 · November 2023 · Paper 1 · Provincial · 4 marks
The circuit diagram below consists of four cells each with a voltage of $1, 5$ V. The resistance of bulbs A, B and C are $3 Ω$ , $6 Ω$ and $8 Ω$ respectively. Use the circuit diagram to answer questions that follow:

When switch S is closed, the reading on the ammeter is $0, 6$ A.
7.3 If the reading on $V_{3}$ is $4, 8$ V, calculate the:
7.3.1 Effective resistance of the circuit(4)
Show the memo (4 ticks)Memo
1. ✓
  Parallel formula $\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}}$
  1 mark · Calculate equivalent resistance
2. ✓
  Substitution $\frac{1}{R _{p}} = \frac{1}{3} + \frac{1}{6}$
  $R_{p} = 2 Ω$
  1 mark · Calculate equivalent resistance
3. ✓
  Series addition $R_{T} = R_{s} + R_{p}$
  $R_{T} = 8 + 2$
  1 mark · Calculate equivalent resistance
4. ✓
  Answer with unit $R_{T} = 10 Ω$
  1 mark · Calculate equivalent resistance
6. Question 8.2.1 · November 2022 · Paper 1 · Provincial · 3 marks
In the circuit diagram below, each cell has a voltage of $1, 5$ V. Use the diagram to answer the questions that follow.
8.2 Calculate the following:
8.2.1 Total resistance of the circuit(3)
Show the memo (3 ticks)Memo
1. ✓
  Parallel resistance $\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \frac{1}{R _{3}}$
  $\frac{1}{R _{p}} = \frac{1}{6} + \frac{1}{4} + \frac{1}{3}$
  $R_{p} = 1, 33 Ω$
  1 mark · Calculate equivalent resistance
2. ✓
  Series total $R_{T} = R_{s} + R_{p}$
  $R_{T} = 2, 67 + 1, 33$
  1 mark · Calculate equivalent resistance
3. ✓
  Answer with unit $R_{T} = 4, 00 Ω$
  1 mark · Calculate equivalent resistance

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