ELECTRICAL ENGINEERING

Resistances in Series When some conductors having resistances R 1 , R 2 , and R 3 etc. are joined end on end as in figure below they are said to be connected in series. It can be proved that the equivalent resistance or total resistance between points A and D is equal to the sum of the three individual resistances. Being a series circuit, it should be kept in mind that figure 1 figure 2 (i) current is the same through all three conductors   (I = I 1 = I 2 = I 3 ) (ii) voltage drop across each is different due to Its resistance and is given by Ohm's Law (iii) sum of the three voltage drops is equal to the voltage applied across the three conductors.  There is a progressive fall in potential as we go from point A to D as shown in Figure 3 figure 3   V = V 1 + V 2 + V 3 = IR 1 + IR 2 + IR 3 But V = IR where R is the equivalent resistance of the series combination. IR=IR 1 + IR 2 + IR 3 R eq =R 1 +R 2 +R 3 Resistances in Parallel Three resistances, as joined in Figure 4

 Ohm's Law This law, which is applicable to electrical conduction through reliable conductors, can be formulated as follows. If the conductor's temperature is constant, the ratio of the potential difference (V) between any two places on it to the current (I) flowing between them will remain constant. What I mean is, V/I = constant, or V/I   = R where R is the resistance of the conductor between the two points considered. Put in another way, It simply means that provided R is kept constant, current is directly proportional to the potential difference across the ends of a conductor. However, this linear relationship between V and I does not apply to all non-metallic conductors. For example, for silicon carbide, the relationship is given by V = KI m   where K and m are constants and m is less   Example 1 : A coil of copper has a resistance of 20 ohm at 10 o C   and is connected to a 220 V supply. By how much must the voltage be Increased in order to maintain current c

Not only resistance but specific resistance or resistivity of metallic conductors also increases With rise in temperature and vice versa. According to the picture below the resistivities of metals vary linearly with temperature over a range of temperature, the variation becoming non-linear both at very high and at very low temperatures. Let, for any metallic conductor, ρ 1  =    resistivity at t 1   o C ρ 2  =    resistivity at t 2   o C m  = slope of the linier part of the curve Next, it is evident that m  = (ρ 2  - ρ 1  ) / (t 2  – t 1  )     or      ρ 2  = ρ 1  +  m  (t 2  – t 1  )   or ρ 2  = ρ 1  [1 + ( m/  ρ 1 ) (t 2  – t 1 )   ] The ratio of m / ρ 1 is called the temperature coefficient of resistivity at temperature t 1 0 C. It may be defined as numerically equal to the fractional change in ρ 1 per 0 C change in temperature from t 1 0 C. It is almost equal to temperature-coefficient of resistance α 1 . therefore, substituting  α 1  =  m / ρ 1,  we get  ρ 2  = ρ 1  [1 + α 1  (t

So far we did not make any distinction between values of α ( alpha)   at different temperatures. But it is found that value of  α ( alpha)  itself is not cönstant, but depends on the initial temperature on which the increment in resistance is based. When the increment is based on the resistance measured at 0 0 C, then α has the value of  α 0   ( alpha nol)  any other initial temperature t 0 C, value of α is α t , and so on. It should be remembered that, for any conductor, α 0 has the maximum value.  Suppose a conductor of resistance R 0   at 0 0 C (point A in Fig. above)  is heated to t o C (point B).  Its resistance R t  after heating is given by  R t   = R 0  (1 +  α 0   t)                                                     … eq (1) where   α 0  is the temperature-coeffcient at 0 0 C. Now, suppose that we have a conductor of resistance  R t  at temperature t 0 C. Let this conductor be cooled from t o C to 0 0 . Obviously, now the initial point is B and the final point is A. The fi

Effect of Temperature on Resistance     we have explain erlier (Law of Resistance) that resistance of the conductor dipending on temprature. so that, here we will show you the effect of rise in temperature:     1) to increase the resistance of pure metal. The increase is large and fairy regular for normal ranges of temperature. The temperature/resistance graph is a straght line (figure 1).     2) to increase the resisrance of alloys, though, in their case, the increase is relatively small and irregular. for some high-resistance alloys like eureka (60% Cu and 40% Ni) and manganin, the increase in resistance is negligible ove a considerable range of temperature.    3) to decrease the resistance of electrolytes, insulators (such as paper, rubber, glass, mica, etc.) and partial conductors such as carbon. hence, insulators are said to prossess a negative temperature-coefisient of resistance. figure 1 ( The temperature/resistance graph) Temperature-Coefficient of Resistance

Law of Resistance Every conductor has resistance that depending on the following factors:     1). it varies direcly as its length, l     2). it varies inversely as the cross-section A of the conductor.     3). it depends on the nature of material.     4). it depending on the temperature of the conductor. Ignoring the last factor fo the time being, we can say that: where: "R" is resistance of the conductor (ohm) "READ : The Unit of Resistance " "l" is the length of the condutor (metre) "A"  is the area of cross section of the conductor (metre^2) is a constant depending on the nature of the material of the conductor known as its specific resistance or resistivity, that will be discussed in Unit of Resistivity from the equetion above, we will know how to get good conductor. good conductors those with little resistace. "READ ALSO: good resistance in Modern Electron Theory ".  statemen 1 the longger the

   The practical unit of resistance is Ohm. A conductor is said to have resistance of one ohm if it permits one ampere current to flow through it when one volt is impressed  across its terminals. Ohm The symbol of ohm is shown below. the ohm symbol Table (multiples and submultiples of Ohm)     For insulator whose resistance are vey high, a much bigger unit is used i.e, mega-Ohm = 10^6 ohm (the prefix 'mega' or 'mego' meaning a million) or kiliohm=10^3 ohm (the prefix 'kilo' meaning thousand). in the case  of vey small resistance , smaller units like miliohm = 10^-3 ohmor microohm = 10^-6 are used. Read also: Resistance  

Figure 1     It may be defined as the property of a substance due to which it opposes the flow of electricity ( Read: The Ide of Electric Potential ) throug it.       Metal (as a class), acids and salt solutions are good conductors of electricity. amongst pure metals, silver, copper, and aluminium are vey good conductors in the given order. This, as discussed earlier (Read: Modern Electron Theory ) , is due to the presence of a large number of free or loosely-attached electrons in their atoms. These vagrant electrons assume a derected motion on the application of an electric potential difference. These electrons while flowing pass throug the molecules or the atoms of the conductor, collide with other atoms and electrons, thereby producing heat.                Figure 2 metal  ( https://www.imperiummultiniaga.com)    Figure 3 copper ( http://www.hoo-tronik.com)     These substances which offer relatively greater difficulty or hindrance to the passage of these elec

     In figure. 1 below is shown a simple voltaic cell. it consists of a copper plate (known as anode) and a zinc plate ( i.e. cathode) immersed in dilute sulphuric acid (H2SO4) contained insuitable vessel. Figure 1 the chemical action taking place within the cell causes the electrons to be remove from Cu plate and to be deposited on the zinc plate at the same time. Thsis transfer of electrons is accomplished through the agency of the diluted H2SO4 which is known as electrolyte. The result is that zinc plate becomes negative due to the deposition of electrons on it and the Cu plate becomes positive due to the departure of electrons  from it. The large number of electrons collected on the zinc rod is being attracted by anode, but is prevented from returning to it by the force set up by the chemical action within the cell. But if the two electrodes are joined by wire externally, then electrons rush to the anode, thereby equalizing the charges of the two electrodes. however due to

     Modern research has ebtablished that all matter whether solid, liquid, or gaseous, consists of minute particles called molecules which are them selves made up of still minute particles known as atoms. Those substances whose molecules consist of similar atoms  are known as elements (as shown in figure 1) Figure 1 (  http://gb.scientificgems.wordpress.com/) and those whose molecules consist of dissimilar atoms are called compounds (as shown in figure 2).  Figure 2 (https://prodiipa.wordpress.com/) An atom is taken to consist of the following:  1).  It has a hard central core known as nucleus. It contains two types of particlesor; one is known as proton and carries positive charge, the other is neutron (discovered by Chadwick in 1932), which is electrically neutral i.e. it carries no charge though it is as haevy as proton. The protons and neutrons are very closely held together with tremendous forces.  2). Revolving round the relatively massive nucleus, in more or