ELECTRICITY
FACTORS ON
WHICH THE RESISTANCE OF A CONDUCTOR DEPENDS
Note the ammeter reading in an electric circuit with
1. A nichrome wire of length l. Assume the reading = 1 A.
2. Nichrome wire of twice the length
(2l). Here, ammeter reading decreases to one-half (0.5 A).
3. A thicker (larger cross-sectional
area) nichrome wire of the same length l.
Here, reading is increased. If the area is doubled, reading is also doubled
(2A).
4. A copper wire of same length and
cross-sectional area as that of first
nichrome wire. Here, reading is changed.
Thus, resistance of a conductor
depends on (i) its length (ii) its area of cross-section and
(iii) nature of material.
Resistance of a uniform metallic
conductor is directly proportional to its length (R ∝ l)
and inversely proportional to the area of cross-section (R ∝ 1/A).
i.e.,
Where ρ
(rho) is a constant of proportionality and is called electrical
resistivity of the material of conductor. It is a characteristic property
of the material.
SI unit of resistivity is Ω
m.
Resistivity of metals & alloys is very low (Range: 10–8 to 10–6 Ω m). They are good conductors of electricity.
Resistivity of insulators (rubber, glass etc.) is very high (Range: 1012 to 1017 Ω m).
Resistance and resistivity vary
with temperature.
Resistivity of an alloy is
generally higher than that of its constituent metals. Alloys do not oxidise
(burn) readily at high temperatures. So, they are used in electrical heating
devices, like electric iron, toasters etc.
Tungsten is used for filaments of
electric bulbs. Copper & aluminium are used for electrical transmission
lines.
Electrical
resistivity of some substances at 20°C
|
Material |
Resistivity (Ω
m) |
|
|
Conductors |
Silver |
1.60 × 10–8 |
|
Copper |
1.62 × 10–8 |
|
|
Aluminium |
2.63 × 10–8 |
|
|
Tungsten |
5.20 × 10–8 |
|
|
Nickel |
6.84 × 10–8 |
|
|
Iron |
10.0 × 10–8 |
|
|
Chromium |
12.9 × 10–8 |
|
|
Mercury |
94.0 × 10–8 |
|
|
Manganese |
1.84 × 10–6 |
|
|
Alloys |
Constantan (Cu + Ni) |
49 × 10–6 |
|
Manganin (Cu + Mn +
Ni) |
44 × 10–6 |
|
|
Nichrome (Ni + Cr + Mn + Fe) |
100 × 10–6 |
|
|
Insulators |
Glass |
1010 – 1014 |
|
Hard rubber |
1013 – 1016 |
|
|
Ebonite |
1015 – 1017 |
|
|
Diamond |
1012 - 1013 |
|
|
Paper (dry) |
1012 |
|
a) How much current will an electric
bulb draw from a 220 V source, if the
resistance of bulb filament is 1200 Ω?
b) How much current will an electric
heater draw from a 220 V source, if the resistance of heater coil is 100 Ω?
Solution:
(a)
V
= 220 V; R = 1200 Ω.
Current, I = V/R
= 220 V/1200 Ω
= 0.18 A.
(b) V
= 220 V, R = 100 Ω.
Current, I = 220 V/100 Ω = 2.2 A.
Thus the current drawn by an
electric bulb and electric heater from the same 220 V source is different.
Problem: The
potential difference between the terminals of an electric heater is 60 V when
it draws a current of 4 A from the source. What current will the heater draw if
the potential difference is increased to 120 V?
Solution:
Potential difference V =60 V, current I = 4 A.
When the potential difference is
increased to 120 V the current is given by
Problem: Resistance
of a metal wire of length 1 m is 26 Ω
at 20°C. If the diameter of the wire is 0.3 mm, what will be the resistivity of
the metal at that temperature? Predict the material of the wire.
Solution:
Resistance R of the wire = 26 Ω
Diameter d = 0.3 mm = 3 × 10-4 m
Length l of the wire = 1 m.
Resistivity of the metallic wire,
ρ =
(RA/l) = (Rπd2/4l).
= 1.84
× 10–6 Ω m.
This is the resistivity of
manganese.
Problem: A wire of given material having length l and area of cross-section A has a resistance of 4 Ω. What would be the resistance of another wire of the same material having length l/2 and area of cross-section 2A?
Solution:
