Electric circuits: Grade 12 Past Paper Questions

The emf of a battery is Ɛ 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 V₁ in terms of the readings on the other voltmeters? A. V₁ = V₂ + V₃. B. V₁ = V₂ + V₃. C. V₁ = V₂ + V₃ + V₄. D. V₁ = V₂ + 2V₃.

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 Rᵧ is TWICE the resistance of Rₓ. When both switches are CLOSED, the reading on the ammeter is 5,5 A. 8.1 Give a reason why there is no current through resistor Rᴢ. 8.2 Calculate the resistance of resistor Rᵧ. 8.3 Calculate the power dissipated by resistor Rₓ. When both switches are now OPENED, the reading on the ammeter is 1,3 A. 8.4 Calculate the reading on the voltmeter. Switch S₁ remains OPEN while switch S₂ is now CLOSED. 8.5 Calculate the reading on the ammeter.

A battery with unknown emf (ɛ) 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. 8.1 State Ohm's law in words. Both switch S₁ and switch S₂ are CLOSED. The reading on ammeter A₁ is 1,5 A. 8.2 Calculate the: 8.2.1 Reading on the voltmeter. 8.2.2 Reading on ammeter A₂. 8.2.3 Power dissipated in the 3 Ω resistor. Switch S₁ is now OPENED, while switch S₂ remains CLOSED. The reading on ammeter A₂ is now 3,64 A. 8.3 Calculate the emf of the battery. Switch S₂ is now OPENED, while switch S₁ is CLOSED. 8.4 How does the voltmeter reading change? Choose from INCREASES, DECREASES or REMAINS THE SAME. Explain the answer.

In the circuit diagram below, Rₓ and Rᵧ are identical ohmic resistors that are connected in parallel. When the switch is open, the ammeter reading is 0,1 A and the voltmeter reading is 3 V. The battery has an unknown emf and internal resistance. What is the reading on the AMMETER and the VOLTMETER when the switch is closed? A. Equal to 0,1 A; equal to 3 V. B. Larger than 0,1 A; equal to 3 V. C. Smaller than 0,1 A; larger than 3 V. D. Larger than 0,1 A; smaller than 3 V.

The battery in the circuit below has an emf of 12 V and internal resistance 0,30 Ω. The resistance of the connecting wires and ammeter can be ignored. 8.1 State Ohm's law in words. 8.2 Determine the: 8.2.1 Total external resistance of the circuit. 8.2.2 Reading on ammeter A. 8.2.3 Current through the 8 Ω resistor. The voltmeter V2 with a very high resistance is now placed between points X and Y, as shown in the diagram below. 8.3 Calculate the reading on the voltmeter. 8.4 When the 8 Ω and 5 Ω resistors alongside point X are removed, the reading on voltmeter V1 increases. Explain this observation. 8.5 The cost of energy is R2,59 per kWh. How many 80 W light bulbs can you have on for 8 hours per day if your budget for lighting is R300 per month? Assume that an average month has 30 days.

The battery in the circuit shown below has an emf of 12 V and an unknown internal resistance r. The resistance of the connecting wires and the ammeter is negligible. Switch S is OPEN. 8.1 Write down the reading on: 8.1.1 Voltmeter V₁. 8.1.2 Voltmeter V₂. Switch S is now CLOSED. The reading on the ammeter is 1,2 A and the power dissipated in resistor X is 5,76 W. 8.2 Define the term power. Calculate the: 8.3 Resistance of resistor X. 8.4 Total EXTERNAL resistance of the circuit. 8.5 Reading on voltmeter V₂. A length of wire of negligible resistance is used to connect point P to point Q in the circuit. 8.6 How will the reading on voltmeter V₁ be affected? Choose from INCREASES, DECREASES or NO EFFECT. Explain the answer.

8.2 Different arrangements of three identical light bulbs X, Y and Z are shown in circuits A, B and C below. The batteries are identical with negligible internal resistance. 8.2.1 In which circuit will bulb X burn the brightest? Choose from A, B or C. Explain the answer. In circuit A, an additional identical light bulb is now connected in parallel to bulb Z. 8.2.2 How will the brightness of bulb X now be affected? Choose from INCREASES, DECREASES or REMAINS THE SAME. Give a reason for the answer.

8.1 A battery with an emf of 24 V and an unknown internal resistance (r) is connected to four resistors. When switch S is closed, the reading on ammeter A₂ is 0,6 A. 8.1.1 Explain what is meant by an emf of 24 V. The power dissipated by the 8 Ω resistor is 46,08 W. 8.1.2 Calculate the resistance of resistor R. 8.1.3 Calculate the internal resistance (r) of the battery. 8.1.4 How does the potential difference across the 4 Ω resistor compare to that across resistor R? Choose from GREATER THAN, LESS THAN or EQUAL TO. Give a reason for the answer. Switch S is now opened. 8.1.5 How will the power dissipated by the 8 Ω resistor now be affected? Choose from INCREASES, DECREASES or REMAINS THE SAME.

10.2 In the circuit below there is a battery with UNKNOWN emf and an internal resistance of 0,5 Ω connected to two resistors of 2 Ω and 6 Ω each as well as a resistor R with unknown resistance. Ignore the resistance of the connecting wires. 10.2.1 State Ohm's Law in words. 10.2.2 Switch S is open. The reading on the voltmeter V₁ is 3 V. Calculate the emf of the battery. 10.2.3 Switch S is closed. The reading on voltmeter V₂ is 10,25 V. Calculate the resistance of the resistor R.

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. 8.1 State Ohm's law in words. When both switches S₁ and S₂ are CLOSED, the reading on ammeter A₁ is 0,8 A. 8.2 Calculate the: 8.2.1 Current through light bulb L. 8.2.2 Reading on ammeter A₂. 8.2.3 Resistance of resistor R. Switch S₂ is now OPENED, while switch S₁ remains CLOSED. 8.3 How will this affect the reading on ammeter A₂? Choose from INCREASES, DECREASES or REMAINS THE SAME. Give a reason for the answer. 8.4 How will the brightness of bulb L be affected? Choose from INCREASES, DECREASES or REMAINS THE SAME. Explain the answer. The letters A to F represent different quantities in the circuit: A is the voltage across the battery, B is the internal resistance of the battery, C is the current through ammeter A₁, D is the current through ammeter A₂, E is the resistance of resistor R, and F is the potential difference across the 9 Ω resistor. Switch S₁ is now OPENED, while switch S₂ is CLOSED. 8.5 Write down the LETTERS of the quantities that will now be equal to zero.

1.9 A learner conducts an experiment by measuring the potential difference and current that flows through three different copper wires, representing the results on graphs X, Y and Z as shown below. Which of the following is TRUE? Resistance of: A. X > Y > Z. B. X = Y = Z. C. Y > X > Z. D. Z > Y > X.

10.1 A group of learners conduct an experiment to determine the emf and internal resistance of a battery by using the circuit below. The learners draw the following potential difference versus current graph from the results acquired. 10.1.1 Give the value of the emf of the battery. 10.1.2 Calculate the internal resistance of the battery. 10.1.3 Determine the external resistance of the circuit when the ammeter reading is Y.

The circuit diagram below shows a battery with an emf of 12 V and an unknown internal resistance, r. The resistance of the ammeters and connecting wires can be ignored. The resistance of the voltmeters is very high. 8.1 Write down the reading on voltmeter V1 when switch S is open. 8.2 The switch S is now CLOSED. The reading on voltmeter V2 is 6 V. Determine the: 8.2.1 Reading on ammeter A1. 8.2.2 Effective resistance of the parallel resistors. 8.2.3 Internal resistance, r, of the battery. 8.2.4 Reading on ammeter A2. 8.3 The cost of electricity is R2,65 per kWh. A 3 500 W electrical oven is used for 50 minutes. Calculate the cost of using the oven for 50 minutes.

QUESTION 8 L1 and L2 are two light bulbs that have the following ratings: L1: 36 W; 20 V and L2: 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. R1 and R2 are resistors. 8.1 Define the term power. 8.2 If both light bulbs operate as RATED, calculate the: 8.2.1 Reading on ammeter A2. 8.2.2 Reading on ammeter A1. 8.2.3 Resistance of resistor R1. 8.2.4 Emf of the battery. 8.3 Bulb L1 burns out after a while. Assume that the resistance of bulb L2 remains constant. Will bulb L2 continue to glow after bulb L1 burns out? Choose from YES or NO. Support your answer with a suitable calculation.

QUESTION 8 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. 8.1 State Ohm's law in words. Switch S is CLOSED. 8.2 The reading on the ammeter is 3,5 A. 8.2.1 Calculate the total external resistance of the circuit. 8.2.2 Calculate the reading on voltmeter V1. 8.2.3 How does the reading on voltmeter V2 compare to the reading on voltmeter V1? Choose from SMALLER THAN, EQUAL TO or GREATER THAN. 8.3 A learner concludes that the emf of the battery is equal to the reading on voltmeter V1. 8.3.1 Define the term emf. 8.3.2 Is the learner's conclusion CORRECT? Choose from YES or NO. 8.3.3 Give a reason for the answer to QUESTION 8.3.2.

Switch S is now removed and replaced by voltmeter V2, as shown in the circuit diagram below. 8.4 How will EACH of the following change? (Choose from INCREASES, DECREASES or REMAINS THE SAME.) 8.4.1 The power dissipated by the 4 Ω resistor. 8.4.2 The reading on voltmeter V1. 8.5 Explain the answer to QUESTION 8.4.2.

1.8 The diagram below represents a circuit in which all the external resistors have the same resistance. Which ONE of the ammeters in the circuit will have the LOWEST reading? A. A₁. B. A₂. C. A₃. D. A₄. 1.9 A simplified diagram of an electrical machine is shown below. What type of machine is this? A. A DC motor. B. An AC motor. C. A DC generator. D. An AC generator.

1.7 Two identically charged spheres, X and Y, carry charges of +2q and −6q respectively. Sphere X experiences an electrostatic force F to the right when the distance between their centres is r. The spheres are brought into contact and are then returned to their original positions. Which ONE of the following represents the magnitude of the electrostatic force that sphere X experiences now? A. F. B. F/4. C. F/12. D. F/3. 1.8 In the circuit diagram below, R₁, R₂ and R₃ are identical resistors. The battery has negligible internal resistance. The power dissipated by R₁ is P. Which ONE of the following is the power dissipated by R₂?

1.9 In the circuit shown below, the switch is open. The reading on the voltmeter is: A. 0 V. B. 6 V. C. 12 V. D. 0,6 V. 1.10 In the circuit below the battery has an emf (ε) and internal resistance r. With switch S open, readings are registered on the ammeter and voltmeter. Switch S is now CLOSED. How do the readings on the ammeter and voltmeter change? B. Ammeter reading increases; voltmeter reading decreases. D. Ammeter reading decreases; voltmeter reading decreases.

1.7 Two identical spheres, P and Q, carry charges of +q and –2q respectively. Sphere P exerts an electrostatic force of magnitude F on sphere Q. Which ONE of the following represents the magnitude of the electrostatic force exerted on sphere P by sphere Q? A. F/2. B. F. C. 2F. D. 4F. 1.8 In the circuit diagram shown below all the resistors are IDENTICAL. Ignore the internal resistance of the cell. Which voltmeter will have the HIGHEST reading when switch S is closed? A. V₁. B. V₂. C. V₃. D. V₄.

1.8 The circuit below was used in a practical investigation. The battery has emf ε and internal resistance r. Ignore the resistance of the connecting wires. Graphs K and L below were obtained from the readings taken. Which ONE of the combinations below CORRECTLY indicates the voltmeter readings taken to obtain graphs K and L? A. Graph K: V₁; Graph L: V₁. B. Graph K: V₁; Graph L: V₂. C. Graph K: V₂; Graph L: V₁. D. Graph K: V₂; Graph L: V₂. 1.9 Which ONE of the following is the function of the split-ring commutator in an electric motor? The split-ring commutator … A. rotates the coil. B. delivers current from the coil to the external circuit. C. ensures that the coil rotates continuously in one direction. D. ensures that the current in the external circuit changes direction.

1.8 The battery in the circuit below has negligible internal resistance. Switch S is closed. Switch S is now opened. How will the readings on the ammeter and voltmeter be affected? D. Ammeter reading increases; voltmeter reading increases. 1.9 The magnitude of the induced emf in an AC generator can be increased by: (i) increasing the strength of the magnetic field, (ii) increasing the speed at which the coil is rotated, (iii) increasing the number of turns in the coil. Which of the statements above are CORRECT? A. (i) and (ii) only. B. (i) and (iii) only. C. (ii) and (iii) only. D. (i), (ii) and (iii).

1.7 Point charges with magnitudes q, 2q, 3q and 4q are placed in different electric fields. The force on each point charge is measured and the results are recorded in the table below: A. a charge of 4q experiences a force of 60 N. B. a charge of q experiences a force of 20 N. C. a charge of 2q experiences a force of 25 N. D. a charge of 3q. Which point charge experiences the greatest electric field strength? 1.8 Two identical light bulbs, P and Q, are connected as shown in the circuit diagram below. The internal resistance of the battery can be ignored. When switch S is closed, which combination best represents the effect on the ammeter reading and the brightness of bulb P: A. reading on ammeter increases, brightness of bulb P stays the same. B. reading on ammeter stays the same, brightness of bulb P increases. C. reading on ammeter stays the same, brightness of bulb P stays the same. D. reading on ammeter increases, brightness of bulb P increases. 1.9 The diagram below shows a coil in a magnetic field. When the coil is part of a DC motor, which ONE of the following must be connected to X and Y: A. split ring (commutator). B. slip rings. C. AC supply. D. soft iron core.

1.7 Two small identical spheres, each with mass m and charge +Q, are placed in a vertical cylinder. The spheres remain stationary when their centres are r metres apart, as shown in the diagram below. Ignore ALL frictional effects. Which ONE of the following expressions can be used to CORRECTLY calculate the distance r? A. √(kQ²/mg). B. √(kmg/Q²). C. √(Q²/kmg). D. √(mg/kQ²). 1.8 The kilowatt-hour (kWh) is a unit of … A. power. B. electric current. C. electrical energy. D. potential difference.