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229
(a) Conductivity :
1. (a) According to Ohms law the electrical resistance of a conductor i.e. the passage of
current is equal to the potential difference, (V) divided by the electric current (I).
V
...(i)
I
(b) The electrical conductance (G) of a solution is the reciprocal of its resistance.
1
G=
...(ii)
R
(c) The electrical resistance (R) of a conductor is linearly proportional to its length (l)
and inversely proportional to its area of cross section (a),
l
a
l
∴
or R = ρ or ρ = R
...(iii)
R∝
a
l
a
The proportionality constant (ρ) is called resistivity of the conductor.
(d) If l = 1m and a = 1m2 then R = ρ
(e) Thus, the resistivity of a conductor (ρ) is defined as the resistance of the conductor
that is 1m long and 1m2 in cross-sectional area.
(f) From eq. (ii) and (iii);
a
1 a
G = × = k×
ρ l
l
The proportionality constant k is called conductivity of the conductor.
1 l
l
×
or k = G =
...(iv)
R a
a
(g) If l = 1m and a = 1m2 then k = G. Thus, conductivity (k) is defined as the
conductance of unit cube of a solution of an electrolyte.
1
(h) Combinations of eq. (iii) and (iv) gives, k =
ρ
Thus, conductivity (k) is the inverse of resistivity (ρ).
2. Unit of various terms :
(a) Unit of (Resistance) R : (SI unit)
V
Volt
R =
=
= ohm (Ω)
Ampere
I
(b) Unit of electrical conductance (G) :
1
1
G =
=
= ohm–1 (Ω–1) or mho
R
ohm
= (reciprocal ohm) Siemens (s)
...(SI unit)
C⎤
⎡
1S = 1Ω–1 = A V–1 = C V–1s–1 ⎢Coulomb (C) = A.s or A = ⎥
s⎦
⎣
∴
R=
Chapter - 4 Electrochemistry
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