Electrical Potential: An object has gravitational potential energy because of its location in a gravitation field. Similarly, a charged object has a potential energy by virtue of its location in an electric field. The unit of measurement of electric potential is Volt (V), so electric potential is often called voltage. A potential of 1volt (V) is equal to 1 joule (J) of energy per coulomb (C) of charge. 1 Volt = [latex]\frac{1 joule}{Coulomb}[/latex]
Electric Current: Electric current is the rate of flow of an electrical charge. It flows from positive to negative. Batteries supply direct current (DC) and the mains supply alternating current (AC).

• The radio and TV require DC and this is obtained from AC mains by means of a rectifier which converts AC into DC.
• Current is a flow of charge, pressured into motion by voltage and hampered by resistance.

Electric Conductors: These are materials that allow charged particles to pass through them easily. Copper, silver and other metals are good conductors for the same reasons that they are good heat conductors, atoms of metals have one or more outer electrons that are loosely bound to their nuclei.
Electric Insulators: The electrons in other materials such as glass and rubber are tightly bound and belong to particular atoms, and it is easy to make them flow.
These materials are poor electrical conductors for the same reasons they are generally poor heat conductors such materials are good insulators.
Semi conductors: Some materials are neither good conductors nor good insulators, they are semiconductors.
Heating effect of electricity: When electricity is passed through thin metallic wires of high resistance, they become high and glow. metals like platinum or tungsten offer resistance to the passage of electric current. The filament of electric bulbs and heater elements is made of such metals which have high resistance.
Fuse Wire: Fuse wire is made of material having low melting point. During short circuiting, the current flowing in the electricity circuit increases instantaneously, if fuse wire is inserted in an electric circuit, it will not allow excess electricity to flow through it. When current exceeds its limit, the fuse wire gets heated, melts and breaks the circuit.
Magnetic Effect of Electricity: It is a phenomenon by which magnetic field is produced by an electric current. A linear current carrying conductor produces a circular magnetic field and a circular current produces a straight magnetic field at the center of the circular coil.
Types of Electricity:
Static Current: It is the electricity produced by friction or rubbing between two dissimilar objects. Depending on the nature of the objects, one acquires positive charge and other the negative charge because of transfer of electrons. For example when a glass rod is rubbed with a silk cloth, some electrons from the rod are transferred to the silk cloth. Thus by losing electrons, the glass rod becomes positively charged and by gaining the number of electrons the silk acquires an equal negative charge. Similarly by rubbing an ebonite comb on hair, a magnetic property is produced which can attract small pieces of paper.
Current Electricity: It is the electricity which brings light and power to our homes. It is of two types. Alternating current which regularly reverses its direction around the circuit and direct current travels without reversing its direction.
Household Wiring System: In Household wiring systems, various electrical devices are connected in a parallel across the power line, which consists of a pair of conductors, one hot and other neutral. An additional ground wire is included for safety.
The maximum permissible current in a circuit is determined by the size of the wires and the maximum temperature they can tolerate. Protection against excessive current and the resulting fire hazard is provided by fuses or circuit breaker.

The materials which allow electric charge (or electricity) to flow freely through them are called conductors.

• Metals are very good conductors of electric charge. Silver, copper and aluminium are some of the good conductors of electricity.


• The materials which do not allow electric charge to flow through them are called nonconductors or insulators.


• For example, most plastics, rubber, non-metals (except graphite), dry wood, wax, mica, porcelain, dry air etc., are insulators.

Coulomb's Law It states that, the electrostatic force of interaction (repulsion or attraction) between two electric charges q1 and q separated by a distance r, is directly proportional to the product of the charges and inversely proportional to the square of distance between them.
[latex]F ∝ q_1 q_2[/latex]
[latex]F ∝[/latex][latex]\frac{1}{r^2}[/latex]
F = k[latex]\frac{q_1q_2}{r^2}[/latex]
K= [latex]\frac{1}{4πε_0}[/latex]
= [latex]9 × 10^9[/latex][latex]\frac{Nm^2}{Coul^2}[/latex]
[latex]⇒[/latex][latex]ε_0[/latex]= [latex]8.85 × 10^{-12}[/latex]
[latex]\frac{Coul^2}{Nm^2}[/latex]

The region surrounding an electric charge or a group of charges in which another charge experiences a force of attraction or repulsion is called 'electric field'.

• The S.I. unit of electric field intensity is N/coul or volt/metre.


• The S.I. unit of electric field intensity is N/coul or volt/metre.

Electric Lines of Force: An electric line of force is that imaginary smooth curve drawn in an electric field along which a free isolated unit positive charge moves. Two lines of force never intersect. If they are assumed to intersect, there will be two directions of electric field at the point of intersection, which is impossible.

Electric Flux(([latex]\phi[/latex])) The total number of electric lines of force through a given area is called the electric flux. open surface [latex]\phi_0 = \int d\phi [/latex]= [latex]\int \vec E .d\vec s[/latex]
or closed surface [latex]\phi_c[/latex] = [latex]\oint \vec E .d\vec s[/latex]
Gauss’s Law: The total electric flux linked with a closed surface is [latex]\frac{1}{ε_0}[/latex]
(Gaussian surface) [latex]\oint \vec E .d\vec s[/latex] = [latex]\frac{q_0}{ε_0}[/latex]

Potential at a point can be physically interpreted as the work done by the field in displacing a unit + ve charge from some reference point to the given point.

• It is a scalar quantity.


• Its dimensions:[latex][M L^2 T^{-3} A^{-1}][/latex]


• Its SI unit is volt or joule coulomb

Equi potential Surfaces: For a given charge distribution, locus of all points having same potential is called equipotential surfaces.

A capacitor or condenser is a device that stores electrical energy. It consists of conductors of any shape and size carrying charges of equal magnitude and opposite signs and separated by an insulating medium The symbol of a capacitor is or The net charge on a capacitor is zero.
Capacitance: Capacitance or capacity of a capacitor is a measure of ability of the capacitor to store charge on it. When a conductor is charged then its potential rises. The increase in potential is directly proportional to the charge given to the conductor.
[latex]Q∝V[/latex] or Q = CV or C = [latex]\frac{Q}{V}[/latex] The constant C is known as the capacitance of the conductor. Its SI unit is farad (F) or coulomb/volt Capacitance of the conductor depends upon: (i) Size of conductor
(ii) Surrounding medium
(iii) Presence of other conductors nearby
Equivalent Capacitance of Capacitors n series:
[latex]\frac{1}{C_eq}[/latex] = [latex]\frac{1}{C_1}[/latex] + [latex]\frac{1}{C_2}[/latex] +.....+[latex]\frac{1}{C_n}[/latex]
In parallel
[latex]C_eq[/latex] = [latex]C_1 + C_2 + ....+ C_n[/latex]

R.J. Van de Graff in 1931 designed an electrostatic generator capable of generating very high potential of the order of V, which was then made use of an accelerating charged particles so as to carry out nuclear reactions.
Principle: It is based on the following two electrostatic phenomena (i) The electric discharge takes place in air or gases readily at pointed conductors.
(ii) If a hollow conductor is in contact with another conductor, then as charge is supplied to the conductor, the hollow conductor continues accepting the charge irrespective of the fact, howsoever large its potential may grow.

The time rate of flow of charge through any cross-section is called electric current. If Dq charge passes through a cross- section in time Dt then, average current av[latex]I_av[/latex] = [latex]\frac{Δq}{Δt}[/latex] Instantaneous current Electric current is measured in ampere (A).
Types of electric current: (a) Direct current: The current whose magnitude and direction does not vary with time is called direct current (dc). The various sources are cells, dc dynamo, etc. Its symbol is (b) Alternating current: The current whose magnitude continuously changes with time and periodically changes. Its direction is called alternating current.

• It has constant amplitude and has alternate positive and negative halves.
• It is produced by ac dynamo.
• Its symbol is

Resistance, Conductance and Resistivity: Resistance (R): It is the property of a substance due to which it opposes the flow of current through it. Its SI unit volt/ampere called ohm [latex]Ω[/latex].
[latex]R∝L[/latex] and [latex]R∝[/latex][latex]\frac{1}{A}[/latex]
so,[latex]R∝[/latex][latex]\frac{L}{A}[/latex]
or, [latex]R∝[/latex]=[latex] ρ[/latex][latex]\frac{L}{A}[/latex]

The reciprocal of specific resistance is conductance i.e. [latex] σ[/latex]= [latex]\frac{1}{ρ}[/latex] where L = length, A = area of cross-section of wire and [latex] ρ[/latex] is called resistivity or The reciprocal of specific resistance is conductance
[latex] σ[/latex]= [latex]\frac{1}{ρ}[/latex]
Superconductors: At a very low temperature, the resistance of the conductor may vanish completely. When it happens, the conductor is called a superconductor. For example, helium is a super conductor at 4.2 K (– 268.8°C).
Ohm’s Law: It states that if the physical state i.e. temperature, nature of material and dimensions of a conductor remain unchanged then the ratio of potential difference applied across its ends to current flowing through it remains constant.
[latex]V∝I[/latex] or V = IR where R= [latex]\frac{V}{I}[/latex] is the resistance of conductor.
Combination of Resistors – Series and Parallel: Series Combination of Resistors: Resistances are said to be connected in series between two points if they provide only a single path between two points.
[latex]R_s[/latex] = [latex]R_1 + R_2 + R_3 + ....+ R_n[/latex] Parallel Combination of Resistors: Resistances are said to be connected in parallel between two points, if it is possible to proceed from one point to another along different paths.
[latex]\frac{1}{R_P}[/latex] = [latex]\frac{1}{R_1}[/latex] + [latex]\frac{1}{R_2}[/latex] + [latex]\frac{1}{R_3}[/latex] +.....+[latex]\frac{1}{R_n}[/latex]

When a current is passed through resistor energy is wasted in overcoming the resistance of the wire. This energy is converted into heat. The heat generated (in joule) when a current of I ampere flows through a resistance of R ohm for T second is given by:[latex]H = I^2RT[/latex]= VIt = [latex]\frac{V^2}{R}[/latex]t joule = [latex]\frac{I^2RT}{4.2}[/latex] calorie This is the joule’s law of heating

• 1 unit of electrical energy = 1 Kilowatt hour (1 KWh) = [latex]3.6 × 10^6 joule[/latex]
This is known as Board of trade (B.O.T) unit of electrical energy.

• Energy liberated per second is called its power.


• The electrical power P delivered or consumed by an electrical device is given by P = VI, where V = Potential difference across the device and I = current.

Ammeter

• An ammeter is a low resistance galvanometer used to measure strength of current in an electrical circuit.


• An ammeter is always connected in series in a circuit because, when an ammeter is connected in series it does not appreciably change the resistance of circuit and hence the main current flowing through the circuit.

Conversion of galvanometer into ammeter: A galvanometer can be converted to an ammeter by connecting a low resistance or shunt in parallel to coil of galvanometer.
Voltmeter

• A voltmeter is a high resistance galvanometer used to measure potential difference.


• A voltmeter is connected in parallel to a circuit element because, when connected in parallel it draws least current from the main current. So it measures nearly accurate potential difference.

Conversion of galvanometer into voltmeter: A galvanometer is converted to a voltmeter by connecting a high resistance in series with the coil of galvanometer.

When an alternating voltage is applied across a coil or a bulb, it sends a similar varying current (i.e., of the same nature as that of voltage) through the coil. The current is called alternating current (A.C.). The current flowing in only one direction in a circuit is called direct current (D.C.). Batteries, thermocouples and solar cells are some of the sources of direct current.
Advantages of Alternating Current over Direct Current: (i) A.C. can be obtained over a wide range of voltages. These voltages can be easily stepped up or stepped down with the help of transformers.
(ii) The generation of A.C. is found to be economical than that of D.C.
(iii) Alternating current can be controlled by using a choke coil without any significant wastage of electrical energy.
(iv) Alternating current may be transmitted at a high voltage from the power house to any place where it can again be brought down to low voltage. The cost in such a transmission is low and energy losses are minimized. Transformers cannot be used for D.C. Hence the cost of D.C. transmission from one place to other is quite high.
(v) A.C. equipments such as electric motors etc are more durable and convenient as compared to D.C. equipment.

It is a device used for transforming a low alternating voltage of high current into a high alternating voltage of low current and vice versa, without increasing power or changing frequency.

Principle: It works on the phenomenon of mutual induction.

If a low voltage is to be transformed into a high voltage, then the number of turns in secondary is more than those in primary. The transformer is called a step up transformer.

If a high voltage is to be transformed into a low voltage, then the number of turns in secondary is less than those in primary. The transformer is called a step-down transformer.

Transformation ratio of the transformer
K = [latex]\frac{Number of turns in secondary N_s }{Number of turns in primary N_p }[/latex] K > 1, for step-up transformer. K < 1, for step-down transformer input power = output power i.e,[latex]E_p × I_p = E_s × I_s [/latex] or [latex]\frac{I^p}{I^s}[/latex]= [latex]\frac{E^s}{E^p}[/latex]= [latex]\frac{N^S}{N^p}[/latex]
Uses of Transformer: A transformer is used in almost all ac operation. (i) In voltage regulators for TV, refrigerator, computer, air conditioner etc.
(ii) In the induction furnaces.
(iii) Step down transformer is used for welding purposes.
(iv) In the transmission of ac over long distance.
(v) Step down and step up transformers are used in electrical power distribution.
(vi) Audio frequency transformers are used in radiography, television, radio, telephone etc.
(vii) Radio frequency transformers are used in radio communication.

Faraday gave two laws of electromagnetic induction.
First law: Whenever there is change in the magnetic flux associated with a circuit, an e.m.f. is induced in the circuit. This is also known as Neumann’s law.
Second law: The magnitude of the induced e.m.f. (e) is directly proportional to the time rate of change of the magnetic flux through the circuit.
e[latex]∝[/latex][latex]\frac{Δ\phi}{Δt}[/latex]
or e = k[latex]\frac{Δ\phi}{Δt}[/latex]
In the S.I. system, emf ‘e’ is measured in volt and [latex]\frac{d\phi}{dt}[/latex] in Wb/sec.
Lenz’s law and Conservation of Energy: According to Lenz’s law, the direction of the induced current is such that it opposes the change in the magnetic flux that causes the induced current or e.m.f. i.e., induced current tries to maintain flux.
On combining Lenz’s law with Faraday’s laws e = -[latex]\frac{d\phi}{dt}[/latex]
The Lenz’s law is consistent with the law of conservation of energy.

The induced circulating current produced in a metal itself due to change in magnetic flux linked with the metal are called eddy current. The direction of eddy currents is given by Lenz’s law
Applications of Eddy Currents:
(1) Dead beat galvanometer.
(2) Energy meter.
(3) Speedometer.
(4) Electric brakes.
(5) Single phase AC motor.
(6) Induction furnace.

Production of induced e.m.f. in a coil due to the changes in current in the same coil, is called self induction. The magnetic flux ([latex](\phi)[/latex] ) linked with the coil is directly proportional to the current (I) flowing through it.
[latex]\phi∝I[/latex]
[latex]\phi[/latex]= LI The constant L is called coefficient of self induction or self inductance of the coil.
The S.I. unit of self inductance or inductance is henry (H). Self-Inductance of a Solenoid [latex]\frac{μ_{0} N^2A}{l}[/latex] Factors on which self inductance depends :If no iron or similar material is nearby, then the value of self-inductance depends only on the geometrical factors (length, cross-sectional area, number of turns and magnetic permeability of free space)
Mutual Inductance: Production of induced e.m.f. in a coil due to the changes of current in a neighboring coil, is called mutual induction. Coefficient of mutual induction or mutual inductance :Let [latex]\phi_{s}[/latex]= magnetic flux linked with the secondary coil when a current Ip flows through the primary coil.
Then, [latex]\phi_{s}∝I_p[/latex] or [latex]\phi_{s}[/latex] = [latex]M I_p[/latex] M = constant of proportionality called mutual inductance or coefficient of mutual induction.

An electrical machine used to convert mechanical energy into electrical energy is known as AC generator/alternator or dynamo. Principle : It works on the principle of electromagnetic induction, i.e., when a coil is rotated in uniform magnetic field, an induced emf is produced in it.
DC Motor: A D.C. motor converts direct current energy from a battery into mechanical energy of rotation. Principle : It is based on the fact that when a coil carrying current is held in a magnetic field, it experiences a torque, which rotates the coil.
Efficiency of the d.c. motor:
[latex]η[/latex] = [latex]\frac{EI}{VI}[/latex]= [latex]\frac{E}{V}[/latex]= [latex]\frac{Back e.m.f.}{Applied e.m.f.}[/latex]
Uses of D.C Motor 1. The D.C. motors are used in D.C. fans (exhaust, ceiling or table) for cooling and ventilation.
2. They are used for pumping water.
3. Big D.C. motors are used for running tram-cars and even trains.