## Voltage and Current Sources

A voltage source is a source of   energy  which establishes a potential difference across its terminals. Most of the sources encountered in everyday life are voltage sources, e.g. batteries, d.c. generators, alternators, etc. The current source is a source of energy that provides a current e.g., collector circuits of transistors. Voltage and current sources are called active elements because they provide electrical energy to a circuit.

Ideal voltage Source

An ideal voltage source is one which maintains a constant terminal voltage, no matter how much current is drawn from it. An ideal voltage source has zero internal resistance.

Practical Voltage Source

A practical voltage source has very low internal resistance, that causes its terminal voltage to decrease when load current is increased and vice-versa.

Ideal Current Source

An ideal current source is one which maintains will supply the same current to any resistance connected across its terminals. An ideal current source has infinite internal resistance.

Practical Current Source

A practical current source has very high internal resistance. Therefore, the load current will change as the value of load resistance changes.

## Fleming’s left and Right Hand Rule

Fleming’s Left Hand Rule

Fleming’s Left-hand Rule. Stretch out the First finger, second finger and thumb of your left hand so that they are at right angles to one another. If the first finger points in the direction of the magnetic field  and second finger points towards the direction of current, then the thumb will point in the direction of motion of the conductor.

Fleming’s Right Hand Rule

Stretch out the forefinger, middle finger and thumb of your right hand so that they are at right angles to one another. If the forefinger points in the direction of the magnetic field, thumb in the direction of motion of the conductor, then the middle finger will point in the direction of induced current. This law is particularly suitable to find the direction of the induced e.m.f. and hence current when the conductor moves at right angles to a stationary magnetic field.

## Types of Resistors

A component whose function in a circuit is to provide a specified value of resistance is called a resistor. The resistors are used to limit the circuit current, divide voltage and in certain cases, generate heat.  Although there are a variety of different types of resistors, the following are the commonly used resistors in electrical and electronic circuits:-

• Carbon composition types
• Film resistors
• Wire-wound resistors
• Cermet resistors

Carbon Composition Type

This type of resistor is made with a mixture of finely ground carbon insulating filler and a resin   binder. The ratio of carbon and insulating filler decides the resistance value. The mixture is formed into a rod and lead connections are made.  The entire resistor is then enclosed in a plastic case to prevent the entry of moisture and other harmful elements from atmosphere. Carbon resistors are relatively inexpensive to build.  However, they are highly sensitive to temperature variations. The carbon resistors are available in power ratings ranging from 1/8 to 2 W.

Film resistors

In a film resistor, a resistive material is deposited uniformly onto a high grade ceramic rod. The resistive film may be carbon (carbon film        resistor) or nickel-chromium (metal film resistor). In these types of resistors, the desired resistance  value is obtained by removing a part of the resistive material in a helical pattern along the rod.

Wire-Wound Resistors

A wire wound resistor is constructed by winding a resistive wire of some alloy around an insulating rod.  It is then enclosed in an insulating cover. Generally, nickel chromium alloy is used because of its very small temperature coefficient of resistance. Wire-wound resistors can safely operate at higher temperatures than carbon types. These resistors have high power ratings ranging from 12 to 225 W.

Cermet resistors

A cermet resistor is made by depositing  a thin film of metal such as nichrome or chromium cobalt on a ceramic substrate.  They are cermet which is a contraction for ceramic and metal.  These resistors have very accurate values. ## Faraday’s Laws of Electromagnetic Induction

Electromagnetic Induction

The phenomenon of production of e.m.f. and hence current in a conductor or coil when the magnetic flux linking the conductor or coil changes is called electromagnetic induction.

There are two laws of electromagnetic induction, that are explained below:-

Faraday’s First Law of Electromagnetic Induction

This law states that, when the magnetic flux linking a conductor or coil changes, an e.m.f. is induced in it. It does not matter how the change in magnetic flux is brought about. The summary of the first law of electromagnetic is that the induced e.m.f. develop in a circuit subjected to a changing magnetic field.

Faraday’s Second Law of Electromagnetic Induction

The magnitude of the e.m.f. induced in a conductor or coil is directly proportional to the rate of change of flux linkage.

## Kirchhoff’s Current Law and Voltage Law

Kirchhoff’s Law are used to solve those networks or circuit where ohms law is may not be readily solved that circuit. Gustav Kirchhoff’s, a German Scientist, summed up his findings in a set of two laws which are called Kirchhoff’s Law. Resistance of a complicated circuits and for calculating the currents flowing in the various branches of circuits or networks. The two laws are Kirchhoff’s current law and Kirchhoff’s voltage law.

Kirchhoff’s Current Law (KCL)

This law relates the currents flowing through the circuit that is why this law is called Kirchhoff’s current law. This law is also known as Kirchhoff’s point law.

This law states that, in any electrical network, the algebraic sum of the currents meeting at a junction or node is always zero.

Lets us consider a case in which few conductors meeting at a junction or point A, where some conductors have current entering to the point and some conductors have currents leaving out the point. Assuming currents entering to the point to be positive while the outgoing currents are negative. We have,

I1-I2-I3+I4+I5=0

I1+I4+I5= I2+I3

Incoming Currents = outgoing Currents

In other words, we can say that incoming current is equal to outgoing current.

Kirchhoff’s Voltage Law (KVL)

This law relates the voltages in a closed circuit of an electrical network. It is also known as Kirchhoff’s mesh law.

Kirchhoff’s voltage law states that the algebraic sum of product of current and resistance in a closed network is equal to the algebraic sum of EMFs in that closed path that is in a closed circuit. V1+V2 = IR1+IR2

∑V = ∑IR = 0 or ∑IR = ∑V

In other way we can say that, in a closed circuit or mesh, the algebraic sum of all the EMFs plus the algebraic sum of products of currents and resistances is zero.

∑V + ∑IR = 0

## Ohm’s Law

Ohm’s Law gives the relation between voltage and current. Whenever an electric potential difference (V) is applied across two points of the conductor, the current (I) flows through it. The flow of current is opposed by the resistance (R) of the conductor. The value of resistance (R) will remain constant for all value of voltages and currents. This relation was expressed first of all by a German Scientist, George Simon Ohm that is why it is called Ohm’s Law. Ohm’s Law states that current flowing between to applied voltage or points of conductor is directly proportional to applied voltage or potential difference between two points of conductor. Provided the temperature and other physical conditions of the conductor do not change.

Mathematically, In other words, Ohm’s Law can also be defined as,

The ratio of potential difference across any two points of a conductor to the current flowing through the conductor is always constant. This constant is called resistance (R). The linear relationship (I α V) does not apply to all non-metallic conductors. For example for silicon carbide, the relationship is given by V = kIX where k and x being constants; x is always less than unity.

Limitations of Ohm’s Law

• Ohm’s Law is not applied to non-linear resistors like vacuum radio value, semiconductors etc.
• It is not applied to arc lamps.
• Electrolytes where enomous gases are produced on either electrode.
• It is not applied to unilateral elements.

Applications of Ohm’s Law

Ohm’s Law applies to linear circuits to find resistance, current and voltages.

## Resistance

It is the property of a substance which restricts the flow of electric current.

We know that current is the flow of electrons, hence resistance is an opposition to the flow of electrons. This opposition occurs due to the presence of large number atoms and molecules.

When current flows through a substance, the free electrons move through the material and collide with atoms and molecules. These collisions cause the electrons to lose some of their energy and it also offer opposition to the flow of electrons. The atomic structure of the substance decides the extent of the  opposition.

Silver, copper and aluminum offer least resistance to flow of current. Tungsten, Nichrome offer very high resistance to flow of current.

The unit of Resistance is ohm (), denoted by R. Factor Affecting Resistance

Resistance of a conductor depends upon the following factors

Length

Resistance of conductor is directly proportional to the length of the conductor. Greater the length, greater the resistance and vice versa.

R α l——————– (i)

Area of Cross Section

Resistance of conductor is inversely proportional to the area of cross section of the conductor. Greater the area of cross section, lesser the resistance and vice versa.

R α 1/a——————– (ii)

Nature of Material

Resistance of the conductor depends upon the nature of the composition of the material of which the conductor is made up. Difference substances have different atomic structures and therefore, offer different resistances for the same length and area of cross section.

Temperature

The resistance of the conductor depends upon the temperature of the conductor. The resistance of the conductor increases with increase in temperature.

From equation (i) and (ii), we get

R α l

R α 1/a

R α l/a

R = ρ l/a

Where P (Rho) is constant of proportionality and it’s called resistivity or specific resistance of the material. P (Rho) refers to the nature of material.

Effect of Temperature on Resistance

• For Metals

The resistance of metals increases with increase in temperature. The graph plotted between temperature and resistance is straight line. The metals have positive temperature co-efficient of resistance.

• For Alloys

The resistance of alloys increases with the increase in temperature but the increase is very small and irregular.

For insulators, electrolytes, semiconductor etc

The resistance of insulators, electrolytes and semiconductors decreases with the rise in temperature. These materials have negative temperature co-efficient of resistance.

## Electric Current

The number of free electrons is available in conductors and semiconductors. In the absence of electric field, these free electrons moves in random directions shown in figure. When an electric field is applied to the conductors and semiconductors, the free electrons start moving in a particular direction and it constitutes an electric current. Definition of electric current

The rate of flow of electric charge through any section of wire is called electric current. The electric current flows if the circuit is closed.

(The SI unit of electric current is Ampere. It is denoted by I)

Conventional current and electron current

Conventional current

The current flows from the positive terminal of the battery to the negative terminal of the battery are called conventional current.

Electron Current

The current flows fro negative terminal of the battery to the positive terminal of the battery is called electron current. In metals, current is caused by electrons and such kind of current is known as electric current.

Types of Electric Current

An electric current is divided into AC current and DC current.

AC Current

AC stands for Alternating Current. Alternating Current changes its direction and magnitude w.r.t. time or at regular intervals. • AC Current can be stepped up or stepped down.
• AC Current can be generated at higher voltage.

DC Current

DC stands for direct current. Direct current has constant magnitude and direction. • DC Current cannot be stepped up or stepped down.
• DC Current cannot be generated at high voltages due to commutation problems.

Properties of Electric Current

Heating Properties

When electric current flows through a high resistive material heat is produced. This property of electric current is used in various heating devices, such as stoves, radiators, water heaters, welding, electric lamps, arc furnaces etc.

Magnetic Properties

When electric current passes through a coil, a magnetic field is produced. Magnetic properties of an electric current are utilized in various electrical machines. Such as electric generators, electric motors, relays etc.

Electrochemical Properties

When electric current passes through an electrolyte, chemical action takes place. The electro-chemical properties of an electric current is utilized in electro-chemical industries for various applications such a electro-plating, electrolytic refining, electro-deposition etc.