ESAT Physics: Electricity and magnetism, set 2

• Answer all questions. No calculator.
• Each question has exactly one correct answer.

1. 11 mark

   Three small charged spheres, P, Q and R, hang from insulating threads, and each carries some charge. It is observed that P and Q repel one another, and that Q and R attract one another. Sphere P carries a negative charge. What can be deduced about the charges on Q and R?

   1. A Q carries a positive charge and R carries a negative charge.
   2. B Q carries a negative charge and R carries a negative charge.
   3. C Q carries a negative charge and R carries a positive charge.
   4. D Q carries a positive charge and R carries a positive charge.
2. 21 mark

   Which one of the following correctly describes some standard circuit symbols?

   1. A A single cell is drawn as two parallel lines of equal length, and a light source used as a circuit component is drawn as a circle containing a cross.
   2. B A single cell is drawn as one long line and one short line, parallel to each other, and a battery is drawn using two or more such long-and-short line pairs placed alongside each other.
   3. C A battery is drawn using exactly the same symbol as a single cell, since a battery is just another name for a cell.
   4. D A light source used as a circuit component is drawn as a circle containing the letter L, in the same style as an ammeter's circle containing the letter A.
3. 31 mark

   Which one of the following correctly describes the magnetic field around a bar magnet?

   1. A Field lines outside the magnet run from the north pole to the south pole, and are more closely spaced near the poles, showing that the field is strongest there.
   2. B Field lines outside the magnet run from the south pole to the north pole, and are more closely spaced near the poles, showing that the field is strongest there.
   3. C Field lines outside the magnet run from the north pole to the south pole, and are most widely spaced near the poles, showing that the field is weakest there.
   4. D Field lines outside the magnet run from the north pole to the south pole, and are equally spaced everywhere, showing that the field strength is the same at every point around the magnet.
4. 41 mark

   A current of 5 A flows through a wire for 3 minutes. What charge flows past a point in the wire during this time?

   1. A 15 C
   2. B 36 C
   3. C 900 C
   4. D 1500 C
5. 51 mark

   Which one of the following lists contains only good electrical conductors?

   1. A Copper, aluminium, glass
   2. B Rubber, copper, aluminium
   3. C Copper, aluminium, plastic
   4. D Copper, graphite, aluminium
6. 61 mark

   Which one of the following correctly compares the magnetic field pattern around a long, straight, current-carrying wire with the field pattern around a current-carrying solenoid?

   1. A The field around the straight wire forms concentric circles centred on the wire; the field around the solenoid resembles that of a bar magnet, with distinct north and south poles at its ends.
   2. B The field around the straight wire resembles that of a bar magnet, with distinct poles at its ends; the field around the solenoid forms concentric circles centred on its axis.
   3. C Both the straight wire and the solenoid produce a field that forms concentric circles centred on the current-carrying conductor.
   4. D Both the straight wire and the solenoid produce a field that resembles that of a bar magnet, with distinct north and south poles.
7. 71 mark

   A 2 ohm resistor and a 3 ohm resistor are connected in series with a battery of emf 10 V (the battery's own resistance can be ignored). What is the potential difference across the 3 ohm resistor?

   1. A 1.5 V
   2. B 4 V
   3. C 5 V
   4. D 6 V
8. 81 mark

   A straight-line graph of potential difference against current is plotted for a fixed resistor held at constant temperature, and passes through the origin. When the current is 0.5 A, the potential difference is 4 V. What would the potential difference be when the current is 1.5 A?

   1. A 3 V
   2. B 5 V
   3. C 8 V
   4. D 12 V
9. 91 mark

   Which one of the following changes to a simple dc electric motor would NOT increase the force on the current-carrying coil, but would instead only reverse its direction?

   1. A Increasing the current flowing through the coil.
   2. B Reversing the direction of the current flowing through the coil.
   3. C Increasing the number of turns on the coil.
   4. D Replacing the magnets with stronger ones.
10. 101 mark

    A technician wants to build a circuit that only operates when its battery is connected the correct way round, and simply stops working, rather than being damaged, if the battery happens to be connected backwards. Which component should be connected in series in the circuit, and why?

    1. A A diode, because it allows current to flow through it easily in one direction only, and blocks current if the battery is reversed.
    2. B An NTC thermistor, because its resistance falls as it warms up, preventing damage if the battery is reversed.
    3. C A light-dependent resistor, because its resistance changes with light level, preventing current from flowing if the battery is reversed.
    4. D A variable resistor, because its resistance can be adjusted to reduce the current if the battery is reversed.
11. 111 mark

    A straight wire carries a current directly from left to right across the page. It lies in a uniform magnetic field that points from the bottom of the page to the top of the page, in the plane of the page. Using Fleming's left-hand rule, what is the direction of the force on the wire?

    1. A Out of the page, towards the reader.
    2. B Into the page, away from the reader.
    3. C Vertically upwards, in the same direction as the field.
    4. D Horizontally, in the same direction as the current.
12. 121 mark

    Three components are connected in series with a 10 V battery of negligible internal resistance. The potential difference across the first component is 2 V, and across the second component is 3 V. What is the potential difference across the third component?

    1. A 2.5 V
    2. B 5 V
    3. C 8 V
    4. D 15 V
13. 131 mark

    A straight wire is moved through a uniform magnetic field so that it cuts through the field lines, inducing a voltage across its ends. Which one of the following changes would reverse the direction, or polarity, of the induced voltage, without changing its size?

    1. A Moving the wire through the field in the opposite direction, at the same speed.
    2. B Moving the wire through the field more quickly, in the same direction.
    3. C Reversing the direction of both the wire's motion and the magnetic field at the same time.
    4. D Using a stronger magnet, with the wire moving in the same direction at the same speed.
14. 141 mark

    A 6 ohm resistor and a 3 ohm resistor are connected in parallel with one another. What is their combined resistance?

    1. A 9 ohms
    2. B 0.5 ohms
    3. C 2 ohms
    4. D 18 ohms
15. 151 mark

    A transformer has 460 turns on its primary coil and 40 turns on its secondary coil. The primary coil is connected to a 230 V ac supply, and the secondary coil delivers a current of 23 A to a heating element. Assuming the transformer is 100 per cent efficient, what current is drawn by the primary coil?

    1. A 0.5 A
    2. B 2 A
    3. C 23 A
    4. D 264.5 A

Worked solutions

Every question below carries the reasoning, not just the answer. The official material for this test publishes a correct option letter and nothing else.

1. Question 1Answer: C

   1. Like charges repel and unlike charges attract.
   2. P and Q repel, so they carry the same type of charge; since P is negative, Q must also be negative.
   3. Q and R attract, so they carry opposite types of charge; since Q is negative, R must be positive.
   4. Therefore the answer is C.
   • Why not A: This treats repulsion as evidence of opposite charge, giving Q a positive charge opposite to P. Like charges repel, so P repelling Q actually means they carry the same type of charge, not opposite types.
   • Why not B: This correctly treats repulsion as evidence of the same charge, giving Q a negative charge matching P, but then wrongly treats attraction the same way for R. Unlike charges attract, so Q attracting R means they carry opposite types of charge, not the same type.
   • Why not D: This gets both rules backwards: it treats repulsion (P and Q) as evidence of opposite charges, and attraction (Q and R) as evidence of the same charge, when repulsion actually indicates the same charge and attraction indicates opposite charges.

2. Question 2Answer: B

   1. A single cell's symbol is one long line and one short line, parallel to one another, representing its two terminals.
   2. A battery's symbol repeats that long-short pair two or more times side by side, showing that several cells are joined together.
   3. A light source used as a circuit component is a separate symbol: a circle containing a cross, not a letter.
   4. Therefore the answer is B.
   • Why not A: This gets the light source symbol right but the single cell wrong: a cell's two lines are of unequal length, one long and one short, not equal length; two equal-length parallel lines is a different symbol altogether.
   • Why not C: This wrongly claims a cell and a battery share one symbol. A battery symbol repeats the long-short line pair two or more times side by side, showing several cells joined together; a single cell symbol has only one such pair.
   • Why not D: This invents a letter-based symbol for a light source. A lamp used as a component is drawn as a circle with a cross inside it, not a circle containing a letter; circles containing letters are used for meters such as the ammeter (A) and voltmeter (V), not for a light source.

3. Question 3Answer: A

   1. Magnetic field lines around a bar magnet point outward from the north pole and into the south pole, so outside the magnet they run from north to south.
   2. Field strength is shown by how closely the lines are spaced: closer lines mean a stronger field.
   3. The lines are closest together near the poles, where the field is strongest, and spread out with increasing distance, where the field is weaker.
   4. Therefore the answer is A.
   • Why not B: This reverses the direction of the field lines. Outside a bar magnet, field lines run from the north pole to the south pole; they complete the loop by running from south back to north inside the magnet.
   • Why not C: This has the spacing backwards: field lines are closest together, not most widely spaced, where the field is strongest, and the field is strongest near the poles, not weakest.
   • Why not D: This wrongly claims the field is uniform. The field lines are closer together near the poles and spread further apart with distance from the magnet, showing that the field weakens away from the poles rather than staying constant.

4. Question 4Answer: C

   1. The relationship between charge, current and time is Q = I x t, and t must be in seconds.
   2. 3 minutes = 3 x 60 = 180 seconds.
   3. Q = 5 x 180 = 900 C.
   4. Therefore the answer is C.
   • Why not A: This uses the time as 3 seconds instead of converting 3 minutes to seconds first; since 1 minute = 60 seconds, 3 minutes is 180 seconds, not 3 seconds.
   • Why not B: This divides time by current (180/5) instead of multiplying current by time; Q = I x t requires multiplication, not division.
   • Why not D: This converts 3 minutes using the wrong conversion factor, treating 1 minute as 100 seconds instead of 60 seconds, giving 300 s instead of 180 s before multiplying by the current.

5. Question 5Answer: D

   1. Metals such as copper and aluminium are good electrical conductors because they contain many free electrons able to move and carry charge.
   2. Graphite, a form of carbon, is unusual in being a good electrical conductor despite not being a metal, again because it has free electrons able to move through it.
   3. Glass, rubber and plastic are all good electrical insulators, since they have very few free electrons able to move.
   4. Therefore the answer is D.
   • Why not A: This includes glass, which is a good electrical insulator, not a conductor.
   • Why not B: This includes rubber, which is a good electrical insulator, not a conductor.
   • Why not C: This includes plastic, which is a good electrical insulator, not a conductor.

6. Question 6Answer: A

   1. The magnetic field around a long straight current-carrying wire forms concentric circles in planes perpendicular to the wire, centred on the wire itself.
   2. A solenoid is a coil of wire, and the fields from its many loops combine so that, outside the coil, the overall field pattern resembles that of a bar magnet, with a north pole at one end and a south pole at the other.
   3. These are genuinely different shapes: one is a set of circles around a single conductor, the other is a pole-to-pole field produced by combining many loops.
   4. Therefore the answer is A.
   • Why not B: This swaps the two patterns round: it is the straight wire that produces concentric circles around it, and the solenoid, formed by coiling the wire, that produces a bar-magnet-like field with poles at its ends.
   • Why not C: This wrongly extends the straight wire's circular pattern to the solenoid as well; coiling the wire into a solenoid combines the individual loops' fields into a bar-magnet-like pattern with poles, not a simple circular pattern.
   • Why not D: This wrongly extends the solenoid's bar-magnet-like pattern to the straight wire as well; a single straight wire has no poles and produces simple concentric circles, not a pattern with distinct ends.

7. Question 7Answer: D

   1. The two resistors are in series, so their resistances add: total resistance = 2 + 3 = 5 ohms.
   2. The current from the battery is I = V/R = 10/5 = 2 A, and this same current flows through both resistors.
   3. The potential difference across the 3 ohm resistor is V = IR = 2 x 3 = 6 V.
   4. Therefore the answer is D.
   • Why not A: This inverts the current formula, calculating total resistance divided by voltage (5/10 = 0.5 A) instead of voltage divided by total resistance (10/5 = 2 A), and then carries this too-small current into V = IR for the 3 ohm resistor.
   • Why not B: This correctly finds the current (10/5 = 2 A) but then applies it to the 2 ohm resistor (2 x 2 = 4 V) instead of the 3 ohm resistor asked for.
   • Why not C: This assumes the supply voltage splits equally between the two resistors (10/2 = 5 V), but in a series circuit the voltage divides in proportion to resistance, not equally, since the two resistors are different sizes.

8. Question 8Answer: D

   1. Since the graph is a straight line through the origin, the resistor obeys R = V/I with a constant resistance.
   2. Using the given point, R = 4/0.5 = 8 ohms.
   3. At a current of 1.5 A, the potential difference is V = IR = 1.5 x 8 = 12 V.
   4. Therefore the answer is D.
   • Why not A: This confuses R = V/I with a multiplying relationship, calculating resistance as 4 x 0.5 = 2 ohms instead of 4/0.5 = 8 ohms, and then uses this wrong resistance in V = IR.
   • Why not B: This assumes that an increase of 1.0 A in current produces an increase of 1.0 V in potential difference, adding the change in current directly onto the original voltage instead of scaling by the resistor's fixed resistance.
   • Why not C: This wrongly treats the change from 0.5 A to 1.5 A as a doubling of the current, and so doubles the voltage to 8 V, when the current has actually tripled.

9. Question 9Answer: B

   1. The magnitude of the force on a current-carrying coil in a magnetic field increases with the current, the number of turns, and the strength of the magnetic field.
   2. Reversing the current's direction does not change any of these three factors, so it does not change the size of the force.
   3. What reversing the current does change is the direction of the force, and so the direction of rotation, by Fleming's left-hand rule.
   4. Therefore the answer is B.
   • Why not A: Increasing the current increases the magnitude of the force on the coil, it does not just reverse its direction, so this is one of the changes that DOES increase the force.
   • Why not C: Increasing the number of turns increases the total force on the coil, since each turn adds to the total force; it does not just reverse the force's direction, so this is another change that DOES increase the force.
   • Why not D: Using stronger magnets increases the magnetic flux density, which increases the force on the coil; it does not just reverse its direction, so this too is a change that DOES increase the force.

10. Question 10Answer: A

    1. The task requires a component whose resistance depends on the direction of current flow through it, not on temperature, light or a manually set value.
    2. A diode has a very low resistance to current flowing one way, and a very high resistance to current flowing the other way.
    3. Connected in series the correct way round, it lets the circuit operate normally; connected with the battery reversed, it blocks the current almost completely, so the circuit simply does not work rather than being damaged.
    4. Therefore the answer is A.
    • Why not B: This picks a thermistor, whose resistance depends on temperature, not on the direction of current flow through it; it conducts equally well whichever way round the battery is connected, so it cannot protect against reversed polarity.
    • Why not C: This picks an LDR, whose resistance depends on light intensity, not on the direction of current flow; like the thermistor, it conducts equally well in either direction, so reversing the battery would not be prevented.
    • Why not D: This picks a variable resistor, which can only change the size of the current, not block it based on direction; a variable resistor conducts equally well in either direction, whatever value it is set to.

11. Question 11Answer: A

    1. The force on a current-carrying wire in a magnetic field, the motor effect, always acts at right angles to both the current direction and the field direction.
    2. Fleming's left-hand rule assigns the First finger to the Field, the seCond finger to the Current, and the thuMb to the resulting force, or motion.
    3. With the field pointing up the page and the current pointing right, the thumb points out of the page, towards the reader.
    4. Therefore the answer is A.
    • Why not B: This gives the opposite direction to the correct one; applying Fleming's left-hand rule correctly, with the First finger along the field (up the page) and the seCond finger along the current (to the right), gives a thuMb direction out of the page, not into it.
    • Why not C: This wrongly assumes the force acts in the same direction as the field. The motor effect force is always perpendicular to both the current and the field, not parallel to either of them.
    • Why not D: This wrongly assumes the force acts in the same direction as the current. Like the field, the current direction and the force direction are perpendicular to one another, not the same.

12. Question 12Answer: B

    1. In a series circuit, the potential differences across all the components add up to the total emf of the battery.
    2. So the third component's potential difference is 10 - 2 - 3.
    3. 10 - 2 - 3 = 5, so the potential difference across the third component is 5 V.
    4. Therefore the answer is B.
    • Why not A: This averages the two known potential differences, (2+3)/2 = 2.5 V, instead of using the fact that all three potential differences must add up to the battery's emf.
    • Why not C: This subtracts only one of the two known potential differences from the battery voltage (10 - 2 = 8 V), forgetting to also subtract the second component's 3 V.
    • Why not D: This adds all three quantities together, 10 + 2 + 3 = 15 V, instead of recognising that the component voltages must add up TO the battery voltage, not add extra ON TO it.

13. Question 13Answer: A

    1. The direction of an induced voltage depends on the direction the wire moves relative to the field, and on the direction of the field itself.
    2. Reversing either one of these on its own reverses the induced voltage's polarity, while leaving its size unchanged if speed and field strength are unchanged.
    3. Reversing the wire's direction of motion alone, with the field and speed unchanged, therefore reverses the polarity without changing the size.
    4. Therefore the answer is A.
    • Why not B: This changes the induced voltage's size, since a faster motion induces a larger voltage, not its direction; the wire is still moving the same way through the same field, so the polarity stays the same.
    • Why not C: This reverses both the direction of motion and the direction of the field at once; each reversal on its own would flip the polarity, so reversing both together cancels out and leaves the polarity unchanged, not reversed.
    • Why not D: This changes the induced voltage's size, since a stronger field induces a larger voltage for the same motion, not its direction, because neither the direction of motion nor the direction of the field has changed.

14. Question 14Answer: C

    1. For two resistors in parallel, 1/R = 1/R1 + 1/R2.
    2. Substituting the values, 1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2.
    3. Taking the reciprocal, R = 1/(1/2) = 2 ohms.
    4. Therefore the answer is C.
    • Why not A: This simply adds the two resistances together, 6 + 3 = 9 ohms, which is the rule for resistors in series, not in parallel; combining resistors in parallel always gives a smaller total resistance than either resistor alone.
    • Why not B: This correctly finds that 1/R = 1/6 + 1/3 = 1/2, but then stops there and gives 1/2 as the answer directly, forgetting that this is 1 divided by the total resistance, not the total resistance itself; the final step of taking the reciprocal, 1/(1/2) = 2, is missing.
    • Why not D: This multiplies the two resistances together, 6 x 3 = 18 ohms, but never divides by their sum, using only the numerator of the product-over-sum shortcut for two resistors in parallel.

15. Question 15Answer: B

    1. The turns ratio gives the secondary voltage: Vs = Vp x (Ns/Np) = 230 x (40/460) = 20 V.
    2. For an ideal, 100 per cent efficient, transformer, power in equals power out: Vp x Ip = Vs x Is.
    3. So Ip = (Vs x Is)/Vp = (20 x 23)/230 = 460/230 = 2 A.
    4. Therefore the answer is B.
    • Why not A: This inverts the power-conservation equation, calculating Vp divided by (Vs x Is) instead of (Vs x Is) divided by Vp, giving a current far too small.
    • Why not C: This assumes the current is unaffected by the transformer, as though only the voltage changes; in fact, an ideal transformer's power is conserved, so a step-down in voltage from 230 V to 20 V must be matched by a corresponding step-up in current, not by an unchanged current.
    • Why not D: This applies the turns ratio to the current in the same direction as it applies to the voltage, multiplying by Np/Ns instead of the opposite way round; because power is conserved, the current ratio is the inverse of the turns ratio, not the same as it.