CURRENT ELECTRICITY

INTRODUCTION

Georg Simon Ohm (16 March 1789 – 6 July 1854) was a German physicist and mathematician. As a high school teacher, Ohm began his research with the new electrochemical ceinvented Using equipment of his own creation, by Italian scientist Alessandro VoltaOhm . found that there is a direct proportionality between the potential difference (voltage) applied across a conductor and the resultant electric current. This relationship is known as Ohm's law.ll,

OHM’S LAW

So long as physicsl state of(material,dimension &temperature) of a conductor remains constant, the electric current flowing through the conductor is directly proportional to potential difference applied across the conductor.

As per Ohm’s law V ∝ I V=IRThis const is resistance of conductor & its S.I unit is Ohm(Ω) I=V/R or R= V/IReciprocal of resistance is conductanceG=1/R its S.I unit is mho or siemen

LIMITATION OF OHM’S LAW

Ohm's law is not a fundamental law of nature. There are a number of commonly used circuit elements which do not obey this law. They have one or more of the following properties:

1. V depends on I non-linearly. 2. The relationship between V and I depends on the sign of V

for the same absolute value of V. 3. The relation between V and I is non-unique, that is, for the

same current I, there is more than one value of voltage V.

The graph shows the characteristics of a device known as a thyristor, which consists of four alternate layers of P and n-type semiconductors. We find that V is not directly proportional to I. All the properties 1 to 3 are seen and the region (PQ) is still more interesting. Here the current carried by the device increases as the voltage decreases. Other examples of non-ohmic devices are electrolytes, thermistors.

RESISTANCE OF CONDUCTOR

The free electrons in a metal are in constant random motion. As they move about they collide with each other and with the atoms of the metal. If a potential difference is now applied across the metal the electrons tend to move towards the positive connection..

The resistance of any conducting material depends on the following factors: (a) the material itself (actually how many free electrons there are per metre cubed) (b) its length (c) its cross-sectional area and (d) its temperature

As they do so their progress is interrupted by collisions. These collisions impede their movement and this property of the material is called its resistance. If the temperature of the metal is raised the atoms vibrate more strongly and the electrons make more violent collisions with them and so the resistance of the metal increase

The resistance of a given piece of material is connected to the current flowing through it and the potential difference between its ends by the equation: Resistance (R) = Potential Difference (V)/ Current (I)

The units of resistance are ohms .

DRIFT VELOCITY

The definition of drift velocity can be understood by imagining the random motion of free electrons inside a conductor. The free electrons inside a conductor moves with random velocities and in random directions. When an electric field is applied across the conductor the randomly moving electrons are subjected to electrical forces along the direction of the field.

Due to this field, the electrons do not give up their randomness of motion but they will be shifting towards higher potential. That means the electrons will drift towards higher potential along with their random motions. Thus every electron will have a net velocity towards higher potential end of the conductor and this net velocity is referred as drift velocity of electrons. The current due to this drift movement of electrons inside an electrically stressed conductor, is known as drift current. It is need less to say that every electric current flows through conductor is drift current

SPECIFIC RESISTANCE

Specific resistance definition: The specific electrical resistance of a conductor depends

on its material and temperature. The Amount of resistance in the flow of current, cross sectional area is called specific resistance of that conductor.

Many resistors and conductors have a uniform cross section with a uniform flow of electric current and are made of one material.

whereR is the electrical resistance of a uniform

specimen of the material (measured in ohms, Ω)

l  is the length of the piece of material (measured in metres, m)

A is the cross-sectional area of the specimen (measured in square metres, m2).

l

the electrical resistivity ρ (Greek: rho) is defined as:

.if and (forming a cube with perfectly-conductive contacts on opposite faces), then the resistance of this element in ohms is numerically equal to the resistivity of the material it is made of in ohm-meters. Likewise, a 1 ohm cm material would have a ⋅resistance of 1 ohm if contacted on opposite faces of a 1 cm×1 cm×1 cm cube.

Conductivity σ (Greek: sigma) is defined as the inverse of resistivity:

Conductivity has SI units of siemens per meter (S/m).

TABLE OF RESISTIVITY FOR SOMEMATERIALS

Material ρ (Ω•m) at 20 °CResistivity

σ (S/m) at 20 °CConductivity

Silver 1.59×10−8 6.30×107

Copper 1.68×10−8 5.96×107

Annealed copper 1.72×10−8 5.80×107

Gold 2.44×10−8 4.10×107

Aluminum 2.82×10−8 3.5×107

Calcium 3.36×10−8 2.98×107

Tungsten 5.60×10−8 1.79×107

Zinc 5.90×10−8 1.69×107

RESISTIVITY

CONDUCTOR

INSULATOR

SEMICONDUCTORS

CLASSIFICATION

TEMPERATURE DEPENDENCE OF RESISTANCE

The temperature coefficient of resistance is a number used to predict how the resistance of a material changes with changes in temperature. Typically the units are either resistance per temperature or 1/temperature depending on which equation is used for the calculations. For example, in copper the temperature coefficient of resistance is about 0.0039 per change in degrees Celsius. A positive temperature coefficient of resistance means that the resistance of the material will increase as temperature increases.

As per the equation or say unit of resistance temperature coefficient, its definition can be given as below:

" Rise in temperature per unit initial resistance, when temperature is raised by one degree Celsius is called the resistance temperature coefficient."

DERIVATION OF TEMPERATURE DEPENDENCE OF RESISTIVITY

The factor by which the resistance of the object changes when changing it’s temperature is called the Temperature coefficient of resistance , Let us derive an mathematical expression and more precise definition of it here:

  Let a conductor have a resistance of  initially at  0, Latter let the

conductor be heated up to t and let it’s resistance at  be Rt. Then the change in the temperature is: t-0 and the change in it’s resistance is: Rt-Ro it is obvious that the change in resistance  depends on following

factors: 1. Directly on it’s initial resistance. 2. Directly on rise in temperature. 3. On the nature of material by which the conductor is made up of.

Or, 

...Read more http://electronicspani.com/temperature-coefficient-of-resistance/

Here the symbol alpha   is a constant multiplier and is known as the temperature coefficient of resistance of the conductor.Solving the equation we get:… /

Solving the equation we get: ...Read more http://electronicspani.com/temperature-coefficient-of-resistance/

Thus the exact definition of the temperature coefficient of resistance is:The increase in resistance per ohm original temperature per degree Celsius change in temperature.Using the formulas derived above and the definition we can find the exact resistance of a substance at any temperature with the following formula:

/

/

It should be noted that all the formulas derived here are equally true for both rise as well as fall in temperature.As temperature of a conductor increases it’s resistance increases and and as thee temperature of conductor is decreased the resistance is also decreases.

GRAPH OF RESISTIVITY VERSUS TEMPERATURE

GRAPH OF RESISTIVITY VERSUS TEMPERATURE FOR DIFFERENT

MATERIALS

THERMISTOR

   Thermistors are temperature sensitive resistors.  All resistors vary with temperature, but thermistors are constructed of semiconductor material with a resistivity that is especially sensitive to temperature.  However, unlike most other resistive devices, the resistance of a thermistor decreases with increasing temperature.  That's due to the properties of the semiconductor material that the thermistor is made from. 

Types of Thermistors:There are mainly 2 types of thermistors namely Positive-temperature coefficient (PTC) and Negative-temperature coefficient (NTC).

CHARACTERISTICS

As just mentioned above, resistance increase with increase in temperature for PTC and resistance decrease with increase in temperature for NTC.

The thermistor exhibits a highly non-linear characteristic of resistance vs temperature.

SUPERCONDUCTIVITY

Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911 in Leiden

DEFINITION:The ability of certain metals or

alloys to conduct an electric current with almost no resistance. Superconductivity usually occurs close to absolute zero, at temperatures approaching -459.67°F (-273.15°C), but has also been observed at temperatures as high as -200°F (-128.88°C)

Critical temperature

1. The temperature of a substance at its critical point.

2. The temperature at which a material becomes a superconductor.

3. The temperature at which a property of a material, such as its magnetism, change

COLOR CODE OF CARBON RESISTOR

TABLE OF COLOR CODE

EXAMPLE

DEFINITION OF EMF AND P.D

The emf of a cell is defined as the work done or energy spent in moving a unit positive charge from its negative terminal to its positive terminal.

Potential difference is defined as the difference in electrical charge between two points in a circuit expressed in volts

Electromotive Force and Internal Resistance

The electromotive force (e) or e.m.f. is the energy provided by a cell or battery per coulomb of charge passing through it, it is measured in volts (V). It is equal to the potential difference across the terminals of the cell when no current is flowing.

•E = energy in joules, J e = electromotive force in volts, V •Q = charge in coulombs, C

Batteries and cells have an  internal resistance (r) which is measures in ohm’s (W). When electricity flows round a circuit the internal resistance of the cell itself resists the flow of current and so thermal (heat) energy is wasted in the cell itself.

•I = current in amperes, A •R = resistance of the load in the circuit in ohms, W •r = internal resistance of the cell in ohms, We = electromotive force in volts, V

We can rearrange the above equation;

and then to

In this equation (V) appears which is the terminal potential difference, measured in volts (V). This is the potential difference across the terminals of the cell when current is flowing in the circuit, it is always less than the e.m.f. of the cell. -

COMBINATION OF CELLS

SERIES COMBINATION When negative terminal of the cell is connected

to the positive terminal of the next cell,then the cell are said to be in series

V=V1 + V2+V3

PARALLEL COMBINATION

Cells are said to be connected in parallel when they are joined positive to positive and negative to negative such that current is divided between the cells.

I=I1+I2+I3

WORK DONE BY ELECTRIC CIRCUIT

Definition:-            This law states that heat produced by

resistor directly depend upon power and time.                                                                       

ORThis law states that heat produced by resistor

directly depend upon current square I2, resistance R and time t.

 

         W= (potential difference) * (charge)

         W= V*I*t ---------------------(since, I=q/t)

  H= W= I2Rt ----------Equation1      (since, V=IR)

JOULE’S LAW

Joule’s law,  in electricity, mathematical description of the rate at which resistance in a circuit converts electric energy into heat energy. The English physicist James Prescott Joule discovered in 1840 that the amount of heat per second that develops in a wire carrying a current is proportional to the electrical resistance of the wire and the square of the current. He determined that the heat evolved per second is equivalent to the electric power absorbed, or the power loss.

When a current of I amperes passes through a circuit of resistance R ohms for a time of t seconds then the heat produced is given by the relation.

H=I2Rt joules

The above relation is known as the joule’s law of heating. It states that the heat produced is proportional to

1.      Square of the current I. 2.      Resistance of the circuit R. 3.      The time t during which the current flows through the circuit. Heat produced in calories can be expressed as                                          H=I2Rt/4.18 Calories                           (1 calorie=4.18 joule)                  

POWER IN AN ELECTRIC CIRCUIT

Electric power, like mechanical power, is the rate of doing work, measured in watts, and represented by the letter P. The term wattage is used colloquially to mean "electric power in watts." The electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential (voltage) difference of V is

whereQ is electric charge in coulombs t is time in seconds I is

electric current in amperes V is electric potential or voltage in volts

Electric power definitionThe electric power P is equal to the energy consumption E divided by the consumption time

P is the electric power in watt (W).E is the energy consumption in joule (J).t is the time in seconds (s).

horsepower - a unit of power equal to 746 watts  H.P., HPpower unit - a measure of electric powerwatt, W - a unit of power equal to 1 joule per second; the power dissipated by a current of 1 ampere flowing across a resistance of 1 ohm