Introduction : Electricity and Magnetism

Charge-

Protons and electrons possess some charge. Proton has positive charge. Electron has negative charge. Neutron does not possess any charge. Like charges repel each other and unlike charges attract each other.

Conductors and Insulators-

Conductors are those materials in which electrons can move freely. All metals are conductors. Insulators do not have any free electrons to move. For example, wood and plastic.

Electric Current-

The flow of electric charge is known as Electric Current. It is expressed in terms of rate of flow of charges.

The SI unit of electric current is Ampere (A).

Direction of electric current is same as direction of positive charges and opposite to the direction of flow of negative charges.

Electric Potential-

The electric potential at a point is defined as work done in bringing a unit positive charge from infinity to that point.

Potential Difference-

The potential difference between two points is defined as the difference in electric potentials at the two given points.

Ohm’s law-

Potential difference between two points is directly proportional to the current, provided temperature is constant.

• Inversely proportional to the area of cross-section.

• Directly proportional to the temperature.

• Depends on nature of material.

Resistivity

• The electrical resistance offered by a substance of unit length and unit cross-sectional area is called resistivity.
  
• Resistivity of metals varies from 10^-8 to 10^-6.
  
• Resistivity of insulators varies from 10¹² to 10¹⁷
  
• Copper and aluminium are used in electrical transmission due to their low resistivity.

Resistance = Resistivity * Length of Conductor/Cross Sectional Area

Superconductors-

Conductors which offer zero resistance to the flow of current are called superconductors.

Combination of resistors-

• Two resistors are said to be combined in series if they carry the same current.

• Two resistors are said to be combined in parallel if the same potential difference is applied to them.

Resistors in series-

When two or more resistors are joined in series, then their total resistance is given by the formula-

  R_S = R₁ + R₂ + R₃

• Voltage across each resistor is given as –

V = V₁ + V₂ + V₃

Resistors in parallel-

• In this case, voltage is same across each resistor and is equal to applied voltage. Total current is given as-

V/R = V/R₁ + V/R₂ + V/R₃

1/R_p = 1/R₁ + 1/R₂ + 1/R₃

Heating effects of Electric Current-

When charge Q moves against the potential difference V in time t, the amount of work is given by

Resistivity

• Heat produced in a resistor is directly proportional to square root of current.

• It is also directly proportional to resistance for a given current.

• Also, directly proportional to time

H = l² Rt

• Filament of electric bulb is made up of tungsten because it has a very high melting point and also does not oxidize readily at a high temperature.

• Electric fuse is a safety device to protect the electrical appliance from short circuit.

Electric Power

• The rate of doing work or rate of consumption of electrical energy is called Electric Power. If W is work done in time t, then P=W/t.

• S.I unit is Watt(W). One watt of power is consumed when 1 A of current flows at a potential difference of 1 V.

• The commercial unit of electrical energy is a kilowatt-hour (kWh).

• 1kWh = 3,600,000J = 3.6×10⁶J

• Represented as P=I²R and P=V²/R

• One kilowatt-hour is defined as the amount of energy consumed when 1kW of power is used for 1 hour.

Magnet

Any substance that attracts iron and iron like objects is defined as magnet. When a wire carries an electric current, it behaves as a magnet.

Properties of Magnet-

• Every magnet has north and south poles.

• Same poles repel each other and unlike poles attract each other.

• A freely suspended magnet will align itself in north south direction, north facing north of the magnet and south facing south of the magnet.

Characteristics of Field Lines

• Field lines arise from north pole and end into south pole of the magnet.

• They are closed curves.

• Field lines never intersect each other.

• Direction of magnetic field lines inside the magnet is from south to north.

Magnetic Field due to current through a Straight Conductor-

• They are represented in the form of concentric circles at every point on conductor.

• Direction of the field is given by compass or right-hand thumb rule. Circles are always closer near the conductor.

Right-hand thumb rule

If a straight conductor is held in the right hand in such a way that the thumb points along the direction of the current, then the tips of the fingers or the curl of the fingers show the direction of magnetic field around it.

Magnetic field due to current through a circular loop-

It is represented by concentric circle at every point. Circle will become larger and larger as one move away.

Factors affecting magnetic field of a circular current carrying conductor-

• Magnetic field is directly proportional to the current passing through the conductor.

• Magnetic field is inversely proportional to the distance from the conductor.

• Magnetic field is directly proportional to number of turns in coil.

Solenoid-

Solenoid is defined as coil of many circular turns of insulated copper wire wrapped closely in a cylindrical form. Magnetic field of solenoid is similar to bar magnet.

Electromagnet-

It is temporary magnet that can be easily demagnetized. In this type of magnet, polarity can be reversed and strength can be varied. They are very strong magnet.

Permanent Magnet-

These types of magnet cannot be easily demagnetized. They are weak magnets in which polarity cannot be reversed.

Force on a current carrying conductor in a magnetic field-

The displacement in the conductor is the maximum when the direction of current is at right angle to the direction of magnetic field.

Flemings Left Hand Rule-

Stretch the thumb, forefinger and middle finger of the left hand such that they are mutually perpendicular. If the forefingers is in the direction of the magnetic field, middle finger in the direction of current then thumb will point in the direction of motion or force

Electric motor

Electric Motor converts electrical energy into mechanical energy.

• Current enters arm AB through brush X and current flows through brush Y from C to D. Using Fleming’s LHR we find that the force pushes AB downwards and pushes CD upwards.

• In an electric motor the split rings PQ act as a commutator that reverses the direction of the current. The reversing of the current is repeated at each half rotation, giving rise to a continuous rotation of the coil.

Electromagnetic Induction-

When we place a conductor in a changing magnetic field, some current is induced in it. This current is known as Induced Current and the phenomenon is known as Electromagnetic Induction.

Fleming Right Hand Rule-

Hold the forefinger, middle finger and thumb of right hand at right angles to each other. Forefinger points towards the direction of magnetic field, thumb points in the direction of motion of conductor and middle finger shows direction of induced current.

Electric generator

• The device that converts mechanical energy into electrical energy.

• Operates on the principle of electromagnetic induction.

AC Generation: The axle attached to the two rings is rotated so that the arms AB and CD move up and down respectively in the produced magnetic field. Thus, the induced current flows through ABCD

• After half rotation the direction of current in both arms changes. Again by applying Fleming’s right hand rule, the induced currents are established in these arms along directions DC and BA, therefore the induced I flows through DCBA.

• DC Generation: They work just like AC, instead use half rings to produce current in one direction only without variations in magnitude.

Domestic Electric Circuits

Three kinds of wires are used in domestic electric circuits.

• Live wire red in colour

• Neutral wire with black insulation cover

• Earth wire with green insulation cover.

The potential difference between live and neutral wire in India is 220V , frequency 50 Hz.

Fuse

• Fuse is a protective device in an electrical circuit in times of overloading.

• Overloading is caused when the neutral and live wire come in contact due to damage to the insulation or a fault in the line.

• In times of overloading the current in circuit increases (short circuit) and becomes hazardous. Joule’s heating (resistive or ohmic heating on the passage of current) in the fuse device melts the circuit and breaks the flow of current in the circuit.

Power loss in transmission-

Power losses in transmission lines over long distances occur due to Joule’s heating. This heat (H) ∝ l²R causes losses, where R is the line resistance.