Electricity and Magnetism: Laws, Rules and PYQs

Electricity and magnetism are one subject, not two, because a current produces a magnetic field and a changing magnetic field produces a current. Almost every science paper in SSC, Railway and Defence exams sets three or four questions from this chapter, usually on a definition, a unit, a rule of direction or a one-step numerical. This note goes through current and potential difference, Ohm's law, resistance, the heating effect, magnets, the magnetic effect of current, induction and the domestic circuit.

Charge, current and potential difference

Electric charge is measured in coulombs. Current is the rate of flow of charge, so the charge that flows is the current multiplied by the time, written as Q equals I into t, and current is measured in amperes with an ammeter connected in series. Conventional current is taken to flow from the positive to the negative terminal outside the cell, opposite to the actual drift of electrons. Potential difference between two points is the work done in moving a unit positive charge from one to the other, so one volt is one joule per coulomb; it is measured with a voltmeter connected in parallel across the two points.

Ohm's law and resistance

Ohm's law states that at a constant temperature the current through a conductor is directly proportional to the potential difference across its ends, which gives V equals I into R. The constant R is the resistance, measured in ohms. Resistance depends on the material and the shape of the conductor: it is directly proportional to the length and inversely proportional to the area of cross section, so a long thin wire resists more than a short thick one. The material property involved is the resistivity, measured in ohm metre. Metals have low resistivity, insulators very high resistivity, and alloys such as nichrome, manganin and constantan have a higher resistivity than the pure metals they are made of, which is why heating elements are made of nichrome and not of copper.

Series and parallel combinations

In a series combination the same current passes through every resistor and the total resistance is the sum of the individual resistances, so the total is always greater than the largest of them. In a parallel combination the same potential difference acts across every resistor, the reciprocal of the total resistance is the sum of the reciprocals, and the total is always less than the smallest of them. Domestic wiring is done in parallel so that each appliance gets the full supply voltage, can be switched independently, and the failure of one does not break the circuit for the others.

Heating effect and electric power

Joule's law of heating says the heat produced in a resistor is proportional to the square of the current, to the resistance and to the time for which the current flows. The electric heater, the electric iron, the geyser, the incandescent bulb and the fuse all work on this effect. The filament of a bulb is made of tungsten because it has a very high melting point and can glow without melting. Electric power is the product of potential difference and current, and can also be written as the square of the current into the resistance, or as the square of the voltage divided by the resistance. Its SI unit is the watt, while the commercial unit of energy is the kilowatt hour, the unit on which the electricity bill is calculated.

Magnets and the magnetic effect of current

A freely suspended bar magnet comes to rest pointing roughly north and south, which is why its ends are called the north seeking and south seeking poles. Like poles repel and unlike poles attract, and magnetic poles always exist in pairs. Magnetic field lines run from the north pole to the south pole outside the magnet and from south to north inside it, forming closed curves; they are crowded where the field is strong and they never intersect, because two directions of the field at one point is impossible. In 1820 Oersted noticed that a compass needle placed near a current-carrying wire is deflected, which proved that a current produces a magnetic field. The direction of that field around a straight conductor is given by the right hand thumb rule: hold the wire in the right hand with the thumb along the current and the curl of the fingers gives the direction of the field. A coil of many turns, or solenoid, behaves like a bar magnet, and a soft iron core inside it makes an electromagnet, which can be switched on and off and is used in cranes, bells and relays.

Motors, induction and generators

A current-carrying conductor placed in a magnetic field experiences a force, and the direction of that force is given by Fleming's left hand rule, in which the forefinger points along the field, the middle finger along the current and the thumb gives the force. This is the principle of the electric motor, which converts electrical energy into mechanical energy. The reverse process is electromagnetic induction, discovered by Michael Faraday in 1831: when the magnetic flux linked with a coil changes, a current is induced in it. The direction of the induced current is given by Fleming's right hand rule, and this is the principle of the electric generator, which converts mechanical energy into electrical energy.

The domestic electric circuit

Household supply in India is alternating current at about two hundred and twenty volts and a frequency of fifty hertz, which means the direction of the current reverses a hundred times a second. Three wires enter the house: the live wire, the neutral wire and the earth wire, which is connected to a metal plate buried in the ground and carries any leakage safely away from the metal body of an appliance. A fuse, or a miniature circuit breaker, is always placed in the live wire so that the appliance is cut off from the supply when the current exceeds the safe value. The two common faults are overloading, when too many appliances draw current together, and a short circuit, when the live and neutral wires touch directly and the resistance falls almost to zero.