Electric Current and Ohm's Law

It should be particularly noted that the direction of electronic current is from zinc to copper in
the external circuit. However, the direction of conventional current (which is given by the direction
of flow of positive charge) is from Cu to zinc. In the present case, there is no flow of positive charge
as such from one electrode to another. But we can look upon the arrival of electrons on copper plate
(with subsequent decrease in its positive charge) as equivalent to an actual departure of positive
charge from it.
When zinc is negatively charged, it is said to be at negative potential with respect to the electrolyte,
whereas anode is said to be at positive potential relative to the electrolyte. Between themselves, Cu
plateis assumed to be at a higher potential than the zinc rod. The difference in potential is continuously
maintainedby the chemical action going on in the cell which supplies energy to establish this potential
difference.
1.4. Resistance
It may be defmed 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 aluminium 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.
Thesevagrant 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.
1.5. The Unit of Resistance
The practical unit of resistance is 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. megaohm =106
ohm (the prefix 'mega' or mego meaning a million) or kilohm = 103ohm (kilo means thousand). In
the case of very small resistances, smaller units like milli-ohm = 10-3 ohm or microhm = 10-6 ohm
are used. The symbol for ohm is Q.
Table 1.1. Multiples and Sub-multiples of Ohm
However. for the same resistance per unit length, cross-sectional area of aluminium conductor has to be
1.6 times that of the copper conductor but it weighs only half as much. Hence, it is used where economy
of weight is more important than economy of space.
** After George Simon Ohm (1787-1854), a German mathematician who in about 1827 formulated the law
of known after his name as Ohm's Law.
Prefix Its meaning Abbreviation Equal to
Mega- One million MO 1060
Kilo- One thousand kO 1030
Centi- One hundredth - -
MiIIi- One thousandth mO 10-30
Micro- One millionth flO 10-<>
Laws of Resistance
The resistance R offered by a conductor depends on the following factors :
(i) It varies directly as its length, I.
(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.
Smaller I
Larger A
Low R
Larger I
Smaller A
Greater R
Fig. 1.3. Fig. 1.4
Neglecting the last factor for the time being, we can say that
R oc ~ or R = P ~ ...(i)
where p is a constant depending on the nature of the material of the conductor and is known as its
specific resistance or resistivity.
If in Eq. (i), we put
I = I metre and A =I metre2,then R =P (Fig. 1.4)
Hence, specific resistance of a material may be defined as
the resistance between the opposite faces of a metre cube of that material.
1.7. Units of Resistivity
From Eq. (i), we have p = AR I
In the S.I. system of units,
A metre2 x R ohm = AR ohm-metre
p = I metre 1
Hence, the unit of resistivity is ohm-metre (Q-m).
It may, however, be noted that resistivity is sometimes expressed as so many ohm per m3.
Although, it is incorrect to say so but it means the same thing as ohm-metre.
If I is in centimetres and A in cm2,then p is in ohm-centimetre (Q-cm).
Values of resistivity and temperature coefficients for various materials are given in Table 1.2.
The resistivities of commercial materials may differ by several per cent due to impurities etc.Resistivities and Temperature Coefficients
Example 1.3. A coil consists of 2000 turns of copper wire having a cross-sectional area of 0.8 J
mm-. The mean length per turn is 80 em and the resistivity of copper is 0.02 J1Q~m. Find the
resistance of the coil and power absorbed by the coil when connected across 110 V d.c. supply.
(F.Y. Engg. Pone Univ. May 1990)
. Solution. Length of the coil, I =0.8 x 2000 =1600 m ; A =0.8 mm2=0.8 x 10-6m2.
R = P~ =0.02X 10-6x 1600/0.8X 10-6=40 Q
Power absorbed = V/ R =1102/40=302.5 W
Example 1.4. An aluminium wire 7.5 m long is connected in a parallel with a copper wire 6 m
long. When a current of 5 A is passed through the combination, it isfound that the current in the
aluminium wire is 3 A. The diameter of the aluminium wire is 1 mm. Determine the diameter of the
copper wire. Resistivity of copper is 0.017 J1Q-m..that of the aluminium is 0.028 J1Q-m.
(F.Y. Engg. Pone Univ. May 1991)
Solution. Let the subscript I represent aluminium and subscript 2 represent copper.
I I R P I a
R I = pi and R2=P2 --1.. :. ...1.=...1.. .1. . -L
al a2 RI PI II a2
RI P2. 12 .
.. a2 = al.R.2 -P'IT 1 ...(1)
Now /1 = 3 A ; /2 =5 - 3=2 A.
If Vis thecommonvoltageacrosstheparallelcombinationof aluminiumandcopperwires,then
Material Resistivity in ohm-metre Temperature coefficient at
at 20.C (x 10-JI) 20.C (x 10-4)
Aluminium, commercial 2.8 40.3
Brass 6-8 20
Carbon 3000 - 7000 -5
Constantan or Eureka 49 +0.1 to-o.4
Copper (annealed) 1.72 39.3
German Silver 20.2 2.7
(84% Cu; 12%Ni; 4% Zn)
Gold 2.44 36.5
Iron 9.8 65
Manganin 44 - 48 0.15
(84% Cu; 12%Mn; 4% Ni)
Mercury 95.8 8.9
Nichrome 108.5 1.5
(60% Cu ; 25% Fe ; 15%Cr)
Nickel 7.8 54
Platinum 9 - 15.5 36.7
Silver 1.64 38
Tungsten 5.5 47
Amber 5 x 1014
Bakelite 1010
Glass 1010 _ 1012
Mica 1015
Rubber 1016
Shellac 1014
Sulphur 1015