Basic Electronics : Resistance

Resistance:
In many materials there is a simple relation between the applied potential difference V across two points and the resulting current I between those points. Such materials are called Ohmic materials, and obey what is called Ohm's law: 


                                                       V = I.R                                              (1.1)

R is a constant called the resistance of the material, which has units of  V/A, or Ohms  ( ).
The resistance depends on the type of material - materials with low resistance are called good conductors, while those with high resistance are good insulators. It also depends on the shape of the material. It is convenient in some circumstances to introduce a quantity called the resistivity, ρ, which depends only on the type of material. If we consider a cylindrical wire of cross-sectional area A and length L, the resistivity is defined as

                                                        R=ρ L/A                                              (1.2)

The units of resistivity are thus  .m.

Resistors in Series:


Suppose in a section of a circuit we encounter a combination of two resistors as in Fig. 1.a :

Figure 1.a : Two resistors in series

These resistors are said to be in series, and as indicated, it is possible to consider them as one single equivalent resistor Req. To find this equivalent resistor, we exploit the fact from energy conservation that  Vac = Vab + Vbc , which using Ohm's law becomes

                                             I.Req = I.R1 + I.R2    Req =R1 +R2 . (1.3)

This is readily extended to the case of multiple resistors in series:

                                               Req = R1 + R2 + ......... + ....... + RN . (1.4)


Resistors in Parallel:

Suppose now in a section of a circuit we encounter a combination of two resistors as in Fig. 1.b :

Figure 1.b : Two resistors in parallel

These resistors are said to be in parallel, and as before, it is possible to consider them as one single equivalent resistor Req. To find this equivalent resistor, we exploit the fact from charge conservation that I = I1 +I2 . Using again Ohm's law , as well as the point that the potential difference across R1 and R2 is the same, we find this becomes

          Vab/Req = Vab/(R1 ) + Vab/R2      ≡   1/Req = 1/(R1 ) + 1/R2                            (1.5)

This also is readily extended to the case of multiple resistors in parallel:

                                             1/Req = 1/(R1 ) + 1/R2 + ⋯ + 1/RN                                                (1.6)