• Define resistivity and conductivity of a conductor
• State the relationship between series and parallel circuits
• Differentiate between series and parallel circuits
2.5 RESISTIVITY AND CONDUCTIVITY
Resistivity
Resistivity ρ of a material is the resistance of unit length of material and unit cross sectional area at a given temperature.
At a given temperature, the resistance R, of a given material is:
• directly proportional to the length of the material, l, and
• inversely proportional to the cross sectional area of the material, A. mathematically, these two statements can be combined and stated as
R = α l
(5.1) A
where ρ is a constant of proportionality known as resistivity of the material, (ρ) is Greek letter pronounced Rho.)
from equation (5.1), we can deduce tha
ρ = R X A Ohm X meter2 = Ohm-meter l meter
We should note that when R is in ohms, A in m2 and l in m, then the unit of ρ is ohm- meter (Ω - m)
Conductivity
The inverse of resistivity is called conductivity and is denoted by the symbol σ. (σ is a Greek letter pronounced sigma) its unit of measurement is (Ω - m)^-1, or 1 .
Mathematically, the two terms can be related as
σ = 1 , (Ω - m)^-1
(5.2) ρ
This relationship can be expressed as follows:
Ω - m
the higher the resistivity of a material, the lower its conductivity, and vice versa.
2.6 SERIES AND PARALLEL CIRCUITS
Series circuits
A series circuit is formed when any numbers of resistors are connected end-to- start so that there is only one path for current to flow. The resistors can be actual resistors or other devices that have resistance like lamps.
Figure (6.1) shows two resistors connected in series (end -to –start) between points A and B.
There is only way for current to get from point A to point B. a series circuit provides only one path for current between two points in a circuit so that the current in the same through R1and R2.
Parallel Circuits
A parallel circuit is formed when any number of resistors are connected starts-to-starts and ends-to-ends so that there is different paths for current to flow. The resistors can be actual resistors or other devices that have resistance like lamps.
Figure (6.3) shows resistors connected in parallel (start-to-start and end-to-end) between points A and B.
There is two ways for current to get from point A to point B. a parallel circuit provides more than one path for current between two points in a circuit so that the current flow in two paths current flow in R1 is called I1 and current flow in R2 is called I2.
In an actual circuits diagram, a parallel circuit may be easy to identify as those in figure (6.3). For example. Figure (6.4) shows Some examples of parallel resistors drawn in other ways.
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