Instantaneous value

Instantaneous value of a time varying wave form

The value of a time varying quantity such as alternating current is not constant and varies with respect to time. The value of such a quantity at an instant of time is called

Kirchhoff’s current law – KCL

Kirchhoff’s current law (KCL) also called Kirchhoff’s first law or Kirchhoff’s junction law states that the sum of currents entering a node in a network is equal to the sum of currents leaving the node. It can also be stated as the algebraic sum of currents at a node is zero.

Here node is a junction of two or more circuit elements connected in a circuit.

Example: consider the following single node network consisting three elements connected to a single node n.

single node network

The i₁ and i₂ are the entering currents and i₃ is the leaving current. The entering currents are indicated by positive value and leaving currents are indicated by negative value. Thus the KCL equation for the node n can be written as,

i₁ + i₂ - i₃ = 0

⇒ i₁ + i₂ = i₃

Law of conservation of electric charge

Kirchhoff’s current law (KCL) is based on the law of conservation of electric charge.

Consider the above equation

i₁ + i₂ = i₃

⇒ \[\frac{dQ_{1}}{dt}+\frac{dQ_{2}}{dt}=\frac{dQ_{3}}{dt}\]

⇒ Q₁ + Q₂ = Q₃.

Alternating Current AC

An electric current in which the periodic reversal of direction of flow of charge particles takes place is called alternating current, in contrast to DC where the flow of electric charge is only in one direction. The waveform of alternating current is usually sinusoidal wave and below figure shows its graphical representation of single phase alternating current.

alternating current

Where T=is the time period

            i=current

            I=peak value of current

This is the form of current used throughout the world in electric power system. The main advantage of an alternating current transmission is the AC voltage can be increased or decreased easily and efficiently with the help of a device called transformer.

With increase in voltage of transmission the power loss reduces whereas the consumer loads at the distribution end are of different voltage levels and also such a high voltage is not safe. This necessitates the changes in the voltage levels at different parts of power system. This can be easily achieved alternating current system with the help of a transformer. Whereas it not possible in system.

Three phase system:

Instead of a single phase system three phase AC system is used has more power transfer capability. In three phase system each single phase is placed at 120 electrical degrees with each other.

Frequency:

Frequency of inverse of time period is depends on the poles in the machine and the speed of the rotation of machine. In a power system all the generators are interconnected and hence their frequencies should be same and they should be run in synchronism with each other throughout the system. The frequency of power system varies from country to country usually 50 Hz or 60 Hz are used. In USA the frequency is 60 Hz, and in India it is 50 Hz. In some countries like Japan mixture of 50 Hz and 60 Hz also used.

Sources of Generation of AC:

Alternator: alternator is a synchronous machine which is the most widely used to generate alternating current and hence its name alternator.

Induction generator: Though induction generators can generate alternating voltages and current, it not used generally as the performance of induction generator is poor. But it is used widely used in wind energy conversion.

Inverter: inverter converts direct current DC to AC. The DC from various sources such as batteries and solar cells can be converted to AC with the help of inverter.

Advantages and disadvantages of AC:

Advantages of AC:

1.         The principle advantage of an AC system is that the level of voltage can easily altered with the help of simple transformer which offers wide range of voltages.

2.         The cost of generation of AC is cheaper than that of an equivalent DC.

3.         The initial cost and maintenance cost of AC machines are cheaper.

4.         AC machines are robust and can almost work in any kind of environment.

5.         Ease of conversion to DC with a rectifier to supply DC loads.

Disadvantages of AC:

1.         Skin effect, in which the charge concentration is more near the surface of the conductor and less at the center of the conductor. This non uniformity in the charge concentration in conductor decreases the effective area of cross section of the conductor thereby the increase in effective resistance.

2.         Analysis and design of AC systems involve complex numbers and is harder when compared with DC analysis which requires simple mathematics.

Direct Current (DC)

The unidirectional flow of electric charge particles is called Direct current or DC. That is the electric current flows in a single direction. When a direct current is passed through a conductor the charge across the area of cross-section is uniform. Direct current is usually abbreviated as DC.

The value of the Direct Current is always constant with respect to time and the below figure shows its graphical representation. Hence in DC circuits the voltage and current are independent on time.

Direct Current (DC)

At the initial stages of development of electrical systems DC is used being used as means of transmission and distribution. Later with the adoption AC with its capability of easy transformation DC system is rarely used.

Sources of Direct Current:

Batteries: batteries are electrochemical energy conversion devices which produce Direct currents.

Solar cells: solar cells or photo voltaic cells convert light energy into electrical energy and they can only generate direct current.

DC Generators: Though DC generators generate DC but they do not generate pure DC instead they generate pulsating voltages. These have to be filtered with the help of filter circuits to get pure DC

Rectifiers: Rectifiers are the devices convert AC to DC

Applications:

Electronics: Most of the electronic devices like mobile phones, computers, radios, televisions, Audio/Video Players, LED lights, electronic watches and calculators etc. work on DC. As the supplies system is alternating current, these devices are powered with the help of rectifiers or run over batteries.

HVDC: For bulk power transmission of electric power over long distance High Voltage Direct Current (HVDC) transmission is used. DC has advantage of less losses and no skin effect.

Electric Vehicles: Electric Vehicles are battery powered vehicles which works on DC.

Rechargeable Batteries: Rechargeable batteries are energy storage devices which require DC input.

Electric Current

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Electric Current

The flow of Electric charge particles is called as electric current. In electric circuits the charge is  carried by the movement of electrons through a conducting material called as conductor.

The loosely bounded electrons that appear in metals are called as conduction electrons. These conduction electrons move freely throughout the metal and they function as charge carriers. Thus in conductors, the current is due to