Course Description
Overview
This course is targeted at Singapore Cambridge GCE O level students, but is also relevant to IGCSE students and Singapore's Integrated program students.
Circuits can seem really confusing the first time you see them. Wires are everywhere and the components are unrecognisable. The good news is that things become a lot easier once you gain a basic understanding of what each part in a circuit does and how it can be connected to other components. This course aims to do just that, allowing you to gain a greater understanding of what's going on in that messy bunch of connected components - you'll even learn to deal with factors such as internal resistance that you can't actually see!
Course Content
You will learn:
- What exactly is current, voltage, charge, power, electromotive force, resistance and the other terms people like to use when talking about circuits
- How the current, voltage, charge, power and other terms people like to use when talking about circuits all relate to each other
- How increasing the number of resistors in a circuit can actually make its resistance go down
- How increasing the amount of energy wasted in a circuit can actually make your battery last longer
- Other weird, wacky, counterintuitive and cool stuff!
A link to the full O level Physics syllabus can be found here
Course Prerequisites
You will need to know:
- How to watch videos on your computer
Math Arena
Course curriculum
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1
Introduction
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Subject Content Requirements
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2
Definitions and Terms - charge and current
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Q1 What is electrical current?
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Q1 explanation
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Q2 What is meant by 5A ?
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Q3 Which is a unit of current?
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Q4 The total amount of charge that passes through a wire's full cross section at any point per unit of time is referred to as ...... ?
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Q5 How much charge flows through the resistor in 4s ?
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Q6 How much charge must pass by a point in 10 s for the current to be 0.50 A?
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Q7 A cell containing 1200 C of charge is connected to a circuit. What is the time taken to discharge the cell given that the current of the circuit is 6 A?
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Q8 There is 100 C of charge stored in a cell. Given that 50% of the charge flows out of the cell in 10 s, what is the average rate of flow of charge out of the cell?
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Q9 A charge of 45C flows through an electric appliance in 3.0 minutes. What is the average current in the appliance?
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Q10 In the circuit below, n charge carriers pass the point P in a time t. Each charge carrier has charge q. The current in the circuit is given by the expression
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3
Definitions and Terms - Voltage, pd and emf
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Q11 Electromotive force is defined as
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Q12 How can one volt also be expressed?
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Q13 If an electric circuit was analogous to a water park, then the battery would be analogous to the ____.
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4
Resistance - Definitions and basics
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Q14 The V-I graph of a wire is given below. What is the resistance of the wire at V= 2 V and V = 10 V?
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Q15 The diagram shows the current I / voltage V graph for a length of resistance wire. Where can Ohm’s law be applied to the wire?
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Q16 Which graph shows how the current changes when the voltage across a fixed resistance is varied?
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Q17 The graph below represents the relationship between potential difference and current for four different resistors. Which resistor has the greatest resistance?
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Q18 A student wants to know the resistance of a conductor when a current I = 0.50 A flows through it. How can he obtain the result?
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Q19 The graph below shows the variation with potential difference V of the current I in an electrical component. Which one of the following is a correct statement about the resistance of the component?
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5
Resistance - Resistivity and resistance
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Q20 A wire which is 2 m long has a resistance of 16 Ω. What is the resistance of this wire if it is 1 m long?
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Q21 Wire A has a resistance of 16 Ω. Wire B has the same dimensions as A but is made from a material which has half the resistivity of wire A. What is the resistance of wire B?
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Q22 A 2 m long wire with a radius of 1 mm has a resistance of 16 Ω. What is the resistance of the same type of wire which is 4 m long and has a radius of 2 mm?
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Q23 Wire A and Wire B have the following ratios. Length LA : Length LB = 5 : 18 Diameter DA : Diameter DB = 2 : 3 Resistivity ρA : Resistivity ρB = 4 : 9 What is the ratio of the resistance of wire A to the resistance of wire B?
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Q24 Wire A and Wire B have the following ratios. Length LA : Length LB = 2 : 1 Diameter DA : Diameter DB = 2 : 3 Resistivity ρA : Resistivity ρB = 4 : 3. Given that the resistance of wire B is 2 Ω, what is the resistance of wire A?
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Q25 A copper wire is part of a complete circuit through which current flows. Which graph best represents the relationship between the wire's length and its resistance?
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Q26 A copper wire of length L and cross-sectional area X has resistance R. A second copper wire at the same temperature has a length of 2L and a cross-sectional area of 0.5 X. What is the resistance of the second copper wire?
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Q27 The diagram below shows a circuit in which a copper wire connects points A and B. The electrical resistance between points A and B can be decreased by
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Q28 The table shows the lengths and diameters of four copper wires. Which wire has the least resistance?
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Q29 A student uses a length of wire as a resistor. He discovers that the resistance of the wire is too small. To be certain of making a resistor of higher value, he should use a piece of wire that is
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Q30 The resistance of a metallic wire conductor is inversely proportional to its
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Q31 In an experiment, four resistance wires made from the same material are connected in turn between the terminals P and Q in the circuit shown. The length and diameter of the wires are different. Which wire will give the smallest reading in the ammeter?
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6
The resistance of metallic conductors
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Q32 To reduce the resistance of a metal conductor one should
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Q33 When a filament lamp is switched on, there is a current in the lamp. As the temperature of the filament rises, its resistance changes. Which pair of graphs shows how the resistance and the current vary with time after the lamp is switched on?
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Q34 Which factors will both increase the resistance of a wire in a circuit?
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Q35 The graph below shows the relationship between the potential difference across a metallic conductor and the electric current through the conductor at constant temperature T1.
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Q36 As the temperature of a metallic conductor increases,
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7
Introduction to Series and Parallel circuits - Series circuits
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Q37 If the e.m.f. of each cell is 1.5 V, what is the voltage across resistor?
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Q38 What is the potential difference across the 3 Ω resistor?
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Q39 The circuit shows three resistors in series connected to a battery. Each resistor has a voltmeter across it and two of the voltages are shown. What is the potential difference (p.d.) across the resistor R?
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Q40 What is the use of the variable resistor in the circuit in the Ohm’s law experiment shown below?
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Q41 In the circuit diagram below, what will happen to the readings in the voltmeter and the ammeter if the variable resistance is increased?
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Q42 The circuit diagram shows four identical resistors connected in a series with a battery. What are the possible readings on voltmeters V1 and V2?
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Q43 A heater has a resistance R when the potential difference across it is 12 V. It is connected in series with a 36 V supply and a resistor S. To ensure that the potential difference across the heater is 12 V, the resistance of S should be
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Q44 A voltmeter of resistance 50 kΩ is connected in a circuit as shown below. The emf of the battery is 12V and the resistance of the resistor is 10 kΩ. The internal resistance of the battery is negligible. The reading of the voltmeter is
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Q45 The circuit contains a battery of e.m.f. 12 V and negligible resistance. What is the potential difference across the 25 Ω resistor?
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8
Introduction to Series and Parallel circuits - Parallel circuits
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Q46 Which of the following is true about point P?
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Q47 The diagram shows a battery of three 1.5V cells. What is an advantage of this arrangement of cells?
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Q48 What is the potential difference across the 1 Ω resistor and the 3 Ω resistor?
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Q49 The diagram shows a circuit. Where must an ammeter be connected to measure the smallest current?
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Q50 What is the current flowing through the cell?
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Q51 What is the current flowing through the resistor R?
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Q52 An electric circuit contains an operating heating element and a lit lamp. Which statement best explains why the lamp remains lit when the heating element is removed from the circuit?
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Q53 Which of the following statements is correct?
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Q54 What is the value of current I?
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Q55 In which one of the circuits below is it possible to vary the current in the lamp by adjusting the variable resistor? The cell has negligible internal resistance.
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Q56 Two lamps X and Y operate at normal brightness when the potential difference across them is 6V. They are connected in parallel to a 4V supply of negligible internal resistance. The filament of lamp X breaks. The filament of lamp Y will
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Q57 In the circuit shown below, the cell has negligible internal resistance. Which of the following equations is correct?
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9
Junctions
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Q58 Point P is a junction in a circuit. What is the current I?
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Q59 The diagram below represents currents in a segment of an electric circuit. What is the reading of ammeter A?
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Q60 Ammeters A1, A2 and A3 are placed in a circuit as shown below. What is the reading on ammeter A3?
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10
Ammeter and voltmeter placement
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Q61 Which diagram shows the arrangement of the ammeter and voltmeter to obtain readings to find the power of a lamp?
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Q62 Which circuit shown below could be used to determine the total current and potential difference of a parallel circuit?
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Q63 A student uses a voltmeter to measure the potential difference across a circuit resistor. To obtain a correct reading, the student must connect the voltmeter
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Q64 Which circuit shows the correct use of meters? (A-ammeter, V-voltmeter)
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Q65 In the circuits represented below, the symbol for the ammeter is A and the symbol for the voltmeter is V. Which diagram represents the proper connections for determining the resistance of the circuit?
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Q66 What quantities may be directly measured by the arrangement of meters shown in the diagram below?
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Q67 In which circuit represented below are meters properly connected to measure the current through resistor R1 and the potential difference across R2?
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Q68 In the circuit below, which meter is not correctly connected?
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11
Calculations involving voltage, current and resistance
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Q69 What is the voltage across the 2 Ω resistor in the circuit shown below?
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Q70 What is the e.m.f. of the cell in the circuit shown below?
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Q71 If 720 C of charge flows through the 2 Ω resistor in 6 min, what is the e.m.f. of the cell?
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Q72 What is the current that flows through the 1 Ω resistor?
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Q73 What is the current that flows through the 6 V cell?
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Q74 Two resistors of resistances 30Ω and 60Ω are arranged in parallel. The current in the 30 Ω resistor is 0.60A. What is the potential difference across the 60Ω resistor?
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Q74 explanation
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Q75 A potential difference (p.d.) across a resistor causes a current in it. The p.d. and the resistance of the resistor can both be changed. Which row shows two changes that will both increase the current in the resistor?
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Q76 A 12 V cell is connected to three resistors arranged in series. What is the voltage across resistor R?
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Q77 In the diagram below of a parallel circuit, ammeter A measures the current supplied by the 110-volt source. The current measured by ammeter A is
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Q78 What is the current in ammeter A in the diagram below?
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12
Effective Resistance - Basics
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Q79 What is the effective resistance of the two resistors in the circuit shown below?
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Q79 explanation
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Q80 What is the effective resistance of the four resistors in the circuit shown below?
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Q81 What is the effective resistance of the three resistors in the circuit shown below?
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Q82 What is the potential difference across the 4 Ω resistor?
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Q83 What is the potential difference across the 3 Ω resistor?
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Q84 A power supply of 18V is connected to three resistors, as shown. What is the potential difference across the 2.0Ω resistor?
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Q85 If the ammeter reading is 2 A and the voltmeter reading is 5 V, what is the e.m.f. of the cell in the circuit?
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Q86 Two identical resistors connected in series have an equivalent resistance of 4 ohms. The same two resistors, when connected in parallel, have an equivalent resistance of
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Q87 When three identical resistors are connected in series, their combined resistance is 6 Ω. What is their combined resistance when they are connected in parallel?
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Q88 A physics student is given three 12-ohm resistors with instructions to create the circuit that would have the lowest possible resistance. The correct circuit would be a
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Q89 In which circuit would ammeter A show the greatest current?
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Q90 Three resistors, each of resistance 6 Ω, are arranged to give a 9 Ω combination across PQ. Which of the following is the arrangement?
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Q91 Three networks X, Y and Z are shown below. Each resistor has the same resistance. Which list shows the network resistances in increasing order of magnitude?
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Q92 The resistors in each of the circuits shown below each have the same resistance. Which of the following gives the circuits in order of increasing total resistance?
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13
Effective Resistance - More complex cases
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Q93 What is the effective resistance of the four resistors in the circuit shown below?
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Q94 What is the resistance of the resistor R?
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Q95 Resistors R1 and R2 have an equivalent resistance of 6 ohms when connected in the circuit shown below. The resistance of R1 could be
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Q96 As the number of resistors in a parallel circuit is increased, what happens to the equivalent resistance of the circuit and total current in the circuit? [Method 1]
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Q96 As the number of resistors in a parallel circuit is increased, what happens to the equivalent resistance of the circuit and total current in the circuit? [Method 2]
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Q97 What is the effective resistance of the nine resistors?
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Q98 What is the value of current I?
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Q99 A resistor can be added to the circuit below to make the current I = 3 A. Which is it?
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Q100 In the circuit shown, the voltmeter has a resistance of 20 kΩ and the battery has an emf of 6.0 V and negligible internal resistance. The reading on the voltmeter is
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Q101 A resistor of resistance 1.0 ohm is connected in series with a battery. The current is 2.0 A. The resistor is now replaced by a resistor of resistance of 4.0 ohms. The current in this circuit is 1.0 A. The internal resistance of the battery is
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14
Jockey Questions
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Q102 A 6.0V battery is connected to a network containing five identical resistors. A voltmeter has one lead connected to point K as shown. At which point should lead L be connected so that the voltmeter reads 3.0V?
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Q103 A 10 Ω resistance wire AB is connected in a circuit as shown. Given that the resistance wire is 2 m long, what is the reading on the voltmeter when the jockey is at point C?
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Q104 A 10 Ω resistance wire AB is connected in a circuit as shown. Given that the resistance wire is 2 m long, what is the reading on the voltmeter when the jockey is at point C?
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Q105 A 10 Ω resistance wire AB is connected in a circuit as shown. Given that the reading of the voltmeter is 0 V when the jockey is at position shown, what is the resistance of the resistor R?
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Q106 A resistance wire AB is connected in a circuit as shown. What happens to the brightness of the lamps as the jockey slides along the resistance wire from point A to point B?
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Q107 In the figure below, AB is a 2 m long resistance wire. When AC = 1.6 m, the galvanometer indicates a zero reading. What is the resistance of R?
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15
Power
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Q108 Three identical resistors of constant resistance are connected in series to a battery of negligible internal resistance. The total power dissipated in the circuit is P. The three resistors are now connected in parallel. The total power dissipated is
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Q109 The element of an electric heater has a resistance R when in operation. What is the resistance of a second heater that has a power output three times as large at the same operating voltage?
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Q110 A conductor of constant resistance dissipates 6.0 W of power when the potential difference across it is 12 V. The power that will be dissipated in this conductor when the potential difference across it is 24 V is
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16
Structured Questions Bundle A
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SQ1 (part 1) Four resistors in a square resistance between points A and C
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SQ1 (part 2) Four resistors in a square resistance between points A and B
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SQ2 (part 1) 24V battery and 2 groups of parallel resistors finding the equivalent resistance
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SQ2 (part 2) 24V battery and 2 groups of parallel resistors calculating the current
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SQ3 (part 1) Sliding contact potential divider calculating the current
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SQ3 (part 2) Sliding contact potential divider voltmeter properties and reading
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SQ3 (part 3) Sliding contact potential divider replacing voltmeter with resistor
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SQ4 (part 1) Lamps X and Y current through each lamp
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SQ4 (part 2) Lamps X and Y voltage and resistance
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SQ4 (part 3) Lamps X and Y current, voltage and resistance through R1
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SQ5 (part 1) 12V battery with 2Ω internal resistance current and voltage in circuit
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SQ5 (part 2) 12V battery with 2Ω internal resistance energy and power dissipated
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SQ6 (part 1) Battery, resistor and 2 lamps circuit in series
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SQ6 (part 2) Battery, resistor and 2 lamps circuit in parallel
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SQ6 (part 3) Battery, resistor and 2 lamps brightness comparison
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SQ7 (part 1) Battery with emf ε and internal resistance r calculating r
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SQ7 (part 2) Battery with emf ε and internal resistance r energy and power
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17
Structured Questions Bundle B
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SQ8 (part 1) Battery with internal resistance connected to variable resistor ε = V + Ir
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SQ8 (part 2) Battery with internal resistance connected to variable resistor graph drawing
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SQ9 (part 1) Connecting resistors effective resistance
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SQ9 (part 2) Connecting resistors window heater
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SQ10 (part 1) Switch in parallel with 60Ω resistor calculating current through ammeter
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SQ10 (part 2) Switch in parallel with 60Ω resistor replacing switch with voltmeter
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SQ11 (part 1) Cells with internal resistance explain why the output voltage is less than the emf
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SQ11 (part 2) Cells with internal resistance cells in a torchlight
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SQ11 (part 3) Cells with internal resistance calculating ε and r from the graph
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SQ12 (part 1) Decorative lamps current, resistance and energy
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SQ12 (part 2) Decorative lamps comparing the set with 10 extra lamps
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SQ13 (part 1) 3Ω, 4Ω and 6Ω resistors largest resistance
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SQ13 (part 2) 3Ω, 4Ω and 6Ω resistors smallest resistance
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SQ13 (part 3) 3Ω, 4Ω and 6Ω resistors effective resistance when connected to 12V battery
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SQ14 (part 1) Battery with internal resistance connected to variable resistor 2 defining emf and calculating voltmeter reading
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SQ14 (part 2) Battery with internal resistance connected to variable resistor 2 drawing graph from data
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Structured Questions Bundle C
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SQ15 (part 1) Potential divider 2 resistor between X and Y
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SQ15 (part 2) Potential divider 2 voltmeter between X and Y
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SQ15 (part 3) Potential divider 2 wire between X and Y
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SQ16 (part 1) Electric car battery pd and current
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SQ16 (part 2) Electric car battery charge and energy
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SQ16 (part 3) Electric car battery effect of internal resistance on current and battery lifespan
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SQ17 (part 1) 30V battery, 3 resistors and 1 lamp finding the effective resistance
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SQ17 (part 2) 30V battery, 3 resistors and 1 lamp circuit calculations
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SQ17 (part 3) 30V battery, 3 resistors and 1 lamp power
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SQ18 (part 1) Car window heating unit resistance
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SQ18 (part 2) Car window heating unit thickness and charge
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SQ19 (part 1) Car battery 2 definitions
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SQ19 (part 2) Car battery 2 circuit calculations
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SQ20 (part 1) Three resistors between terminals A and B calculating the total resistance
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SQ20 (part 2) Three resistors between terminals A and B pd and current calculations
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SQ21 Car battery 3
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19
Structured Questions Bundle D
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SQ22 (part 1) 4 cells and 3 resistors resistance and emf
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SQ22 (part 2) 4 cells and 3 resistors current and charge
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SQ22 (part 3) 4 cells and 3 resistors determining which cell will go flat first
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SQ23 (part 1) Explanations question emf and output voltage
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SQ23 (part 2) Explanations question why is low internal resistance important
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SQ24 (part 1) Non-ohmic components semiconducting diode and filament lamp
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SQ24 (part 2) Non-ohmic components resistance and power dissipated by a filament lamp
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SQ25 (part 1) Thermistor question drawing the experimental setup
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SQ25 (part 2) Thermistor question experimental procedure
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SQ25 (part 3) Thermistor question pd across thermistor in a circuit
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SQ25 (part 4) Thermistor question current in the circuit
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SQ25 (part 15 Thermistor question resistance of fixed resistor
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SQ25 (part 1) Thermistor question effect of the battery having internal resistance
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SQ26 (part 1) Thermistor question 2 voltage across 540Ω resistor
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SQ26 (part 2) Thermistor question 2 voltage across 1200Ω resistor and effective resistance of resistor and thermistor
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SQ26 (part 3) Thermistor question 2 resistance of the thermistor
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SQ26 (part 4) Thermistor question 2 effect of temperature on pd across 1200Ω resistor
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SQ27 (part 1) Resistors W, X, Y and Z calculating total resistance from V and I
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SQ27 (part 2) Resistors W, X, Y and Z other circuit calculations
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SQ28 (part 1) Current-time graph for filament lamp determining maximum current from graph
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SQ28 (part 2) Current-time graph for filament lamp resistance and power of lamp at normal operating temperature
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SQ28 (part 3) Current-time graph for filament lamp explanation for decreasing current
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SQ28 (part 4) Current-time graph for filament lamp changes to the current when connecting a second lamp to the supply
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Structured Questions Bundle E
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SQ29 (part 1) 9V battery with internal resistance calculating pd between points A and B
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SQ29 (part 2) 9V battery with internal resistance energy transformed by battery and energy dissipated in internal resistance
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SQ30 (part 1) Battery with internal resistance connected to variable resistor 3 explain why terminal pd decreases as current increases
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SQ30 (part 2) Battery with internal resistance connected to variable resistor 3 finding ε from graph
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SQ30 (part 3) Battery with internal resistance connected to variable resistor 3 finding r from graph
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SQ30 (part 4) Battery with internal resistance connected to variable resistor 3 drawing new lines on the graph
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SQ30 (part 5) Battery with internal resistance connected to variable resistor 3 circuit calculations
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SQ31 (part 1) Battery with internal resistance connected in parallel to 2Ω resistor and R calculating pd
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SQ31 (part 2) Battery with internal resistance connected in parallel to 2Ω resistor and R current and resistance
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SQ31 (part 3) Battery with internal resistance connected in parallel to 2Ω resistor and R conservation of energy
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SQ32 (part 1) Light-dependent resistor question current and voltage
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SQ32 (part 2) Light-dependent resistor question changes in light intensity
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SQ33 (part 1) Three resistors and thermistor calculating total resistance and current
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SQ33 (part 2) Three resistors and thermistor voltage between different points
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SQ34 (part 1) Lamps P and Q current in the battery
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SQ34 (part 1) Lamps P and Q resistance of P and Q
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SQ34 (part 1) Lamps P and Q series arrangement
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