Electricity and Magnetism: Laws, Rules and PYQs

The correct answer is D, it gets halved. By Ohm's law, at a constant temperature the current through a conductor is directly proportional to the potential difference across its ends, since the current equals the potential difference divided by the resistance. The resistance of the conductor does not change when the voltage is changed, so halving the potential difference halves the current exactly.

Option A is wrong because a smaller driving voltage cannot push a larger current through the same resistance. Option B is wrong for the same reason, and it describes what would happen if the voltage were doubled rather than halved. Option C, that the current gets decreased, is true as far as it goes but it is not the best answer, because the question can be answered exactly: the current does not merely fall, it falls to one half. In a question of this kind always give the precise proportional change rather than the vague direction of change.

The correct answer is B, potential difference. The potential difference between two points in a circuit is defined as the work done in moving a unit positive charge from one point to the other. From this definition comes the unit: one volt is one joule of work per coulomb of charge, and the quantity is measured with a voltmeter connected in parallel across the two points.

Option A, pressure distance, is not a physical quantity at all, and pressure belongs to mechanics rather than to circuits. Option C, potential distance, is likewise not a defined term; the word potential appears only to make the option look plausible. Option D, pressure difference, is a real quantity but belongs to fluids, where it drives the flow of a liquid or a gas; it is sometimes used only as an analogy for voltage while teaching, never as the name of the electrical quantity. The definition asked for is that of potential difference.

The correct answer is D, microwave. A microwave oven does not cook by passing a current through a resistance. It generates microwaves in a magnetron, and these waves make the water molecules in the food rotate rapidly, so the food heats from within by dielectric heating. The heating effect of current plays no part in the cooking itself.

Option A, the electric heater, works exactly on Joule heating: current through a nichrome element produces heat proportional to the square of the current, the resistance and the time. Option B, the filament bulb, passes current through a thin tungsten wire that becomes white hot and glows, which is the same effect taken to a very high temperature. Option C, the electric iron, again uses a coiled resistance element inside the sole plate. Since three of the four are ordinary resistance heating devices, the microwave oven is the odd one out.

The correct answer is C, 6000 ohm. By Ohm's law the resistance equals the potential difference divided by the current. Here the current must first be converted into the base unit: two milliampere is 0.002 ampere. Dividing twelve volt by 0.002 ampere gives six thousand ohm, that is six kilo-ohm.

Option A, 600 ohm, is what you get if the milliampere is mistaken for a hundredth of an ampere instead of a thousandth, a common slip under time pressure. Option B, 6 ohm, is the answer to a different question, namely twelve volt divided by two ampere, and it ignores the prefix milli altogether. Option D, 60 ohm, does not follow from the numbers at all and is there only to fill the choice. The lesson is to convert every prefix, milli, micro, kilo or mega, into the base unit before dividing.

The correct answer is A, tungsten. Tungsten has the highest melting point of all metals, well above three thousand degrees Celsius, so a thin tungsten wire can be heated until it glows white without melting. It also has a fairly high resistivity and a low rate of evaporation at working temperature, which is why the filament lasts for hundreds of hours inside a bulb filled with an inert gas.

Option B, silver, is the best conductor of electricity of all metals, but for that very reason it would produce hardly any heat, and it melts at a temperature far too low for a filament. Option C, nichrome, is the right choice for the element of a heater or a toaster, where a red heat is wanted, but it cannot reach the white heat needed to give useful light. Option D, copper, is used for connecting wires precisely because it has a low resistance and stays cool while carrying current.

The correct answer is B, the right hand thumb rule, also called Maxwell's corkscrew rule. Hold the conductor in your right hand with the thumb stretched along the direction of the conventional current; the way your fingers curl round the wire is the direction of the concentric magnetic field lines. The field is strongest close to the wire and weakens with distance.

Option A, Fleming's left hand rule, gives the direction of the force on a current-carrying conductor placed in a magnetic field, which is the principle of the electric motor, not the shape of the field around a wire. Option C, Fleming's right hand rule, gives the direction of the current induced in a conductor moved in a magnetic field, the principle of the generator. Option D, Lenz's law, states that the induced current opposes the change that produced it, which again concerns induction. Only the right hand thumb rule answers the question asked.

The correct answer is B. In Fleming's left hand rule the forefinger, the middle finger and the thumb of the left hand are held at right angles to one another: the forefinger points along the magnetic field, the middle finger along the current, and the thumb then gives the direction of the force. It is the rule behind the electric motor, which converts electrical energy into mechanical energy.

Option A describes Fleming's right hand rule, which is used for the generator, and interchanging the two rules is the single commonest mistake in this chapter. Option C is found instead by the right hand thumb rule applied to each turn of the coil, which shows that a solenoid behaves like a bar magnet. Option D is not a matter of direction in space at all: a potential difference is measured with a voltmeter and needs no hand rule. Remember the pair, left hand for the motor and right hand for the generator.

The correct answer is B, Michael Faraday. In 1831 Faraday showed that when the magnetic flux linked with a closed coil changes, whether by moving a magnet, moving the coil or changing the current in a nearby coil, a current is induced in it. This discovery is the basis of the generator, the transformer and almost the whole of electrical power engineering.

Option A, Oersted, made the complementary discovery eleven years earlier, in 1820, when he found that a compass needle is deflected near a current-carrying wire, showing that a current produces a magnetic field. Option C, Volta, invented the voltaic pile, the first electric battery, and the volt is named after him. Option D, James Watt, was an engineer of the steam engine and gave his name to the unit of power, but he had nothing to do with induction. The pair worth fixing in memory is Oersted in 1820 and Faraday in 1831.

The correct answer is B, in the live wire. The fuse is a short piece of wire of low melting point placed in series in the live line, so that an excessive current melts it and breaks the circuit. Because the break is made on the live side, the appliance is left completely disconnected from the high potential and is safe to handle.

Option A is wrong because a fuse in the neutral wire would indeed stop the current, but the appliance would remain joined to the live wire and anyone touching it could still receive a shock. Option C is wrong because the earth wire is a safety path to the ground and must never carry a fuse, as breaking it would remove the very protection it provides. Option D is wrong because a fuse placed in parallel would short the appliance instead of protecting it; a fuse is always in series with the load it protects.

The correct answer is B. The tangent drawn to a magnetic field line at any point gives the direction of the field at that point. If two lines crossed, two different tangents could be drawn at the point of crossing, which would mean the compass needle placed there would have to point in two directions at once. Since that is impossible, field lines never intersect.

Option A is wrong because the field being zero is a different situation, called a neutral point, where no line passes at all rather than two crossing. Option C is beside the point: field lines are indeed a way of picturing the field, but even as a picture they must show one direction at each point, so being imaginary is not the reason. Option D states a true fact, that a magnet always has both poles and a single pole cannot exist, but it explains why lines are closed curves and not why they cannot cross.

The correct answer is C, the kilowatt hour. It is the energy consumed by an appliance of one kilowatt working for one hour, and it equals three point six million joules. The electricity meter in a house counts these units, which is why the kilowatt hour is often called simply a unit of electricity.

Option A, the watt, is the SI unit of power, that is the rate of using energy, not of energy itself, so it cannot appear on a bill as a quantity consumed. Option B, the volt ampere, is also a unit of power, used for apparent power in alternating current work, and again measures a rate. Option D, the joule per second, is just another name for the watt and so has the same problem. Only the kilowatt hour multiplies power by time and therefore measures energy.

The correct answer is C. The resistance of a wire equals the resistivity of the material multiplied by the length and divided by the area of cross section. A longer wire gives the electrons a longer path and more collisions, so the resistance rises with length; a thicker wire gives them more room, so the resistance falls as the area grows.

Option A reverses the dependence on thickness, which is why a thin wire heats up more than a thick one carrying the same current. Option B reverses the dependence on length. Option D is wrong because only the resistivity, not the resistance, is independent of the size of the specimen; resistivity is a property of the material and changes only with the substance and its temperature. A useful check: doubling the length doubles the resistance, while doubling the diameter makes the area four times larger and cuts the resistance to a quarter.