Electrical Resistance
Electrical resistance definition and calculations.
Resistance definition
Resistance is an electrical quantity that measures how the device or materially reduces the electric current flow through it.
The resistance is measured in units of ohms (Ω).
If we make an analogy to water flow in pipes, the resistance is bigger when the pipe is thinner, so the water flow is decreased.
Resistance calculation
The resistance of a conductor is the resistivity of the conductor's material times the conductor's length divided by the conductor's cross-sectional area.
R is the resistance in ohms (Ω).
ρ is the resistivity in ohms-meter (Ω×m)
l is the length of the conductor in meter (m)
A is the cross-sectional area of the conductor in square meters (m2)
It is easy to understand this formula with water pipes analogy:
- when the pipe is longer, the length is bigger and the resistance will increase.
- when the pipe is wider, the cross-sectional area is bigger and the resistance will decrease.
Resistance calculation with ohm's law
R is the resistance of the resistor in ohms (Ω).
V is the voltage drop on the resistor in volts (V).
I is the current of the resistor in amperes (A).
Temperature effects of resistance
The resistance of a resistor increases when the temperature of the resistor increases.
R2 = R1 × ( 1 + α(T2 - T1) )
R2 is the resistance at temperature T2 in ohms (Ω).
R1 is the resistance at temperature T1 in ohms (Ω).
α is the temperature coefficient.
Resistance of resistors in series
The total equivalent resistance of resistors in series is the sum of the resistance values:
RTotal = R1+ R2+ R3+...
Resistance of resistors in parallel
The total equivalent resistance of resistors in parallel is given by:
Measuring electrical resistance
Electrical resistance is measured with the ohmmeter instrument.
In order to measure the resistance of a resistor or a circuit, the circuit should have the power supply turned off.
The ohmmeter should be connected to the two ends of the circuit so the resistance can be read.
Superconductivity
Superconductivity is the drop of resistance to zero at very low temperatures near 0ºK.
The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current which flows through it: If the resistance is constant over a considerable range of voltage, then Ohm's law, I = V/R,
Resistors can be broad of two types. Fixed Resistors and Variable Resistors. resistors. A fixed resistor is one for which the value of its resistance is specified and cannot be varied in general.
(a) resistor, (b) rheostat (variable resistor), and (c) potentiometer
Types of resistors :
Carbon Composition Resistor.
Thermistor.
Wire Wound Resistor.
Metal Film Resistor.
Carbon Film Resistor.
Variable Resistor.
Varistor
Light Dependent Resistor.
Always read resistors from left to right. - Resistors never start with a metallic band on the left. If you have a resistor with a gold or silver band on one end, you have a 5% or 10% tolerance resistor. Position the resistor with this band on the right side and again read your resistor from left to right.
| COLOUR | 1ST Digit | 2nd Digit | 3rd Digit | MULTIPLIER |
| Black | 0 | 0 | 0 | 100 |
| Brown | 1 | 1 | 1 | 101 |
| Red | 2 | 2 | 2 | 102 |
| Orange | 3 | 3 | 3 | 103 |
| Yellow | 4 | 4 | 4 | 104 |
| Green | 5 | 5 | 5 | 105 |
| Blue | 6 | 6 | 6 | 106 |
| Violet | 7 | 7 | 7 | 107 |
| Grey | 8 | 8 | 8 | 108 |
| White | 9 | 9 | 9 | 109 |
| Gold |
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| Silver |
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| None |
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It may be defined as the property of a substance due to which it opposes (or restricts) the flow of electricity (i.e., electrons) through it.
Metals (as a class), acids, and salts solutions are good conductors of electricity. Amongst pure metals, silver, copper, and aluminum are very good conductors in the given order.* This, as discussed earlier, is due to the presence of a large number of free or loosely-attached electrons in their atoms. These vagrant electrons assume a directed motion on the application of an electric potential difference. These electrons while flowing pass through the molecules or the atoms of the conductor, collide and other atoms and electrons, thereby producing heat.
Those substances which offer relatively greater difficulty or hindrance to the passage of these electrons are said to be relatively poor conductors of electricity like
bakelite, mica, glass, rubber, p.v.c. (polyvinyl chloride) and dry wood etc. Amongst good insulators can be included fibrous substances such as paper and cotton when dry, mineral oils free from acids and water, ceramics like hard porcelain and asbestos, and many other plastics besides p.v.c. It is helpful to remember that electric friction is similar to friction in Mechanics.
The Unit of Resistance
The practical unit of resistance is the ohm.** A conductor is said to have a resistance of one ohm if it permits one ampere current to flow through it when one volt is impressed across its terminals.
For insulators whose resistances are very high,a much bigger unit is used i.e., mega-ohm = 106 ohm (the prefix‘mega’ or mego meaning a million) or kilo-ohm = 103 ohm (kilo meansthousand). In the case of very small resistances, smaller units like milli-ohm = 10-3 ohm or micro-ohm = 10-6 ohm are used. The symbol for ohm is Ù.
| Table 1.1. Multiples and Sub-multiples of Ohm | |||
| Prefix | Its meaning | Abbreviation | Equal to |
| Mega- | One million | M Ù | 106 Ù |
| Kilo- | One thousand | k Ù | 103 Ù |
| Centi- | One hundredth | – | – |
| Milli- | One thousandth | m Ù | 10-3 Ù |
| One millionth | μ Ù | 10-6 Ù | |
Laws of Resistance
The resistance R offered by a conductor depends on the following factors :
(i) It varies directly as its length, l.
(ii) It varies inversely as the cross-section A of the conductor.
(iii) It depends on the nature of the material.
(iv) It also depends on the temperature of the conductor.
| Table 1.2. Resistivities and Temperature Coefficients | ||||
| Material | Resistivity in ohm-metre at 20ºC (´ 10-8) | Temperature coefficient at 20ºC (´ 10-4) |
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| Aluminum, commercial | 2.8 | 40.3 |
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| Brass | 6 – 8 | 20 |
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| Carbon | 3000 – 7000 | -5 |
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| Constantan or Eureka | 49 | +0.1 | to | -0.4 |
| Copper (annealed) | 1.72 | 39.3 |
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| German Silver | 20.2 | 2.7 |
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| (84% Cu; 12% Ni; 4% Zn) |
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| Gold | 2.44 | 36.5 |
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| Iron | 9.8 | 65 |
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| Manganin | 44 – 48 | 0.15 |
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| (84% Cu ; 12% Mn ; 4% Ni) |
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| Mercury | 95.8 | 8.9 |
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| Nichrome | 108.5 | 1.5 |
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| (60% Cu ; 25% Fe ; 15% Cr) |
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| Nickel | 7.8 | 54 |
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| Platinum | 9 – 15.5 | 36.7 |
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| Silver | 1.64 | 38 |
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| Tungsten | 5.5 | 47 |
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| Amber | 5 ´ 1014 |
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| Bakelite | 1010 |
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| Glass | 1010 – 1012 |
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| Mica | 1015 |
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| Rubber | 1016 |
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| Shellac | 1014 |
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| Sulphur | 1015 |
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Tutorial Problems No. 1.1 1. Calculate the resistance of 100 m length of a wire having a uniform cross-sectional area of 0.1 mm2 if the wire is made of manganin having a resistivity of 50 ´ 10-8 Ù-m. If the wire is drawn out to three times its original length, by how many times would you expect its resistance to be increased ? [500 Ù; 9 times] 2. A cube of a material of side 1 cm has a resistance of 0.001 Ù between its opposite faces. If the same volume of the material has a length of 8 cm and a uniform cross-section, what will be the resistance of this length ? [0.064 Ù] 3. A lead wire and an iron wire are connected in parallel. Their respective specific resistances are in the ratio 49 : 24. The former carries 80 per cent more current than the latter and the latter is 47 per cent longer than the former. Determine the ratio of their cross-sectional area. [2.5 : 1] 4. A rectangular metal strip has the following dimensions : x = 10 cm, y = 0.5 cm, z = 0.2 cm Determine the ratio of resistances Rx, Ry, and Rz between the respective pairs of opposite faces. [Rx : Ry : Rz : 10,000 : 25 : 4] (Elect. Engg. A.M.Ae. S.I.) 5. The resistance of a conductor 1 mm2 in cross-section and 20 m long is 0.346 Ù. Determine the specific resistance of the conducting material. [1.73 ´ 10-8 Ù-m] (Elect. Circuits-1, Bangalore Univ. 1991) 6. When a current of 2 A flows for 3 micro-seconds in a coper wire, estimate the number of electrons crossing the cross-section of the wire. (Bombay University, 2000) Hint : With 2 A for 3 μ Sec, charge transferred = 6 μ-coulombs Number of electrons crossed = 6 ´ 10-6/(1.6 ´ 10-19) = 3.75 ´ 10+ 13 |
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