In this article we will discuss about the meaning and laws of resistance to electric current.
Meaning of Resistance:
Resistance may be defined as that property of a substance which opposes (or restricts) the flow of an electric current (or electrons) through it.
The practical as well as mks (or SI) unit of resistance is ohm (Ω), which is defined as that resistance between two points of a conductor when a potential difference of one volt, applied between these points, produces in this conductor a current of one ampere, the conductor not being a source of any emf.
For insulators having high resistance, much bigger unit’s kilo-ohm or kΩ (103 ohm) and mega-ohm or MΩ (106 ohm) are used. In case of very small resistances smaller units like milli-ohm (10-3 ohm) or micro- ohm (10-6 ohm) are employed.
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Each resistor has two main characteristics i.e., its resistance value in ohms and its power dissipating capacity in watts. Resistors are employed for many purposes such as electric heaters, telephone equipment, electric and electronic circuit elements, and current limiting devices. As such their resistance values and tolerances and their power rating vary widely. Resistors of 0.1 Ω to many mega-ohms are manufactured.
Acceptable tolerances may range from ± 20% (resistors serving as heating elements) to ± 0.001 percent (precision resistors in sensitive measuring instruments). The power rating may be as low as 1/10 W and as high as several hundred watts.
Since no single resistor material or type can be made to encompass all the required ranges and tolerances, many different designs are available. Most common commercially available resistors with their properties are given in Table 1.1.
The value of R is selected to have a desired current I or permissible voltage drop I R. At the same time wattage of the resistor is selected so that it can dissipate the heat losses without getting itself overheated. Too much heat may burn the resistor.
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From the operating conditions point of view the resistors can be broadly classified into two categories viz., fixed and variable (or adjustable) resistors.
(a) Fixed Resistors:
The symbols for fixed resistors used in circuit diagrams are given in Fig. 1.8 (a).
(b) Variable or Adjustable Resistors:
For circuits requiring a resistance that can be adjusted while it remains connected in the circuit (such as the volume control on a radio), variable resistors are required. They usually have three leads, two fixed and one movable.
If contacts are made to only two leads of the resistor (stationary lead and moving lead), the variable resistor is being used as a rheostat. The symbols for a rheostat are given in Fig. 1.8 (b). Rheostats are usually employed to limit current flowing in circuit branches.
If all the three contacts are employed in a circuit, it is termed a potentiometer or “pot”. Pots are often used as voltage dividers to control or vary voltage across a circuit branch. The symbols for “pots” are given in Fig. 1.8 (c). Thus the potentiometer (or the pot) is a three terminal resistor with an adjustable sliding contact that functions as an adjustable voltage divider and makes it possible to mechanically vary the resistance.
Laws of Resistance:
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The resistance of a wire depends upon its length, area of x-section, type of material, purity and hardness of material of which it is made of and the operating temperature.
Resistance of a wire is:
(a) Directly proportional to its length, I i.e., R a I
(b) Inversely proportional to its area of x-section, a
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i.e., R α I/a
Combining above two facts we have R α l/a
Or R = ρ l/a
Where ρ (rho) is a constant depending upon the nature of the material and is known as the specific resistance or resistivity of the material of the wire.
To determine the nature of the constant ρ let us imagine a conductor of unit length and unit cross-sectional area, for example a cube whose edges are each of length one unit, and let the current flow into the cube at right angles to one face and out at the other face. Then putting l = 1 and a = 1 in Eq. (1.8) we have R = ρ. Hence resistance of a material of unit length having unit cross-sectional area is defined as the resistivity or specific resistance of the material.
Specific resistance or resistivity of a material is also defined as the resistance between opposite faces of a unit cube of that material.
Resistivity is measured in ohm-metres (Ω-m) or ohms per metre cube in mks (or SI) system and ohm- cm (Ω-cm) or ohm per cm cube in cgs system.
1 Ω-m = 100 Ω-cm
The reciprocal of resistance i.e. 1/R is called the conductance and is denoted by English letter G. It is defined as the inducement offered by the conductor to the flow of current and is measured in Siemens (S). Earlier, the unit of conductance was mho (ʊ).
1 Siemen = 1 mho
From Eq. (1.8)
Where σ = 1/ρ and is known as specific conductance or conductivity of the material. Hence conductivity ρ is the reciprocal of the resistivity and is defined as the conductance between the two opposite faces of a unit cube. The unit of conductivity is Siemens/metre (S/m).
Example 1:
A coil consists of 2,000 turns of copper wire having a cross-sectional area of 0.8 mm2. The mean length per turn is 80 cm, and the resistivity of copper is 0.02 µ Ω-m. Find the resistance of the coil.
Solution:
Length of the coil, I – Number of turns × mean length per turn
= 2,000 × 0.8 = 1,600 m
Cross-sectional area of wire, a = 0.8 mm2 = 0.8 × 10-6 m2
Resistivity of copper, ρ = 0.02 µΩ-m = 2 × 10-2 × 10-6 Ω-m = 2 × 10-8Ω-m
Resistance of the coil, R = l/a = 2 × 10-8 × 1,600 / 0.8 × 10-6 = 40 Ω Ans.
Example 2:
A heater element is made of nichrome wire having resistivity equal to 100 × 10-8 Ω- m. The diameter of the wire is 0.4 mm. Calculate the length of the wire required to get a resistance of 40 Ω.
Solution:
Resistance of nichrome wire, R = 40 Ω
Resistivity of nichrome wire, ρ = 100 × 10-8Ω-m
