536
12 Electric Circuits
where L is the length of the conductor. Unit of resistivity is m.
Electrical Conductance (σ )
σ = 1/ρ
(12.5)
The units of conductance are mho/m.
Variation of Resistance and Resistivity with Temperature
R t = R 0 (1 + αT )
(12.6)
ρ t = ρ 0 (1 + αT )
(12.7)
where α is the temperature coefficient of resistance or resistivity.
Resistors in Series
R =
n
R n
(12.8)
Resistors in Parallel
1
R
=
n
1
R n
(12.9)
Joule’s law: The power (P) developed is given by
P = i
2 R = i V = V
2
/R
(12.10)
Cells
Cells in series: If n cells each of emf ξ and internal resistor r are connected in series
then the current in the circuit is given by
i =
nξ
R + nr
(12.11)
where R is the external resistance.
Cells in parallel: In this case the total emf is that of a single cell ξ . As the internal
resistances of the cells are in parallel, the equivalent internal resistance is r/n, with
the external resistance R in series. The current is
i =
ξ
R + r/n
(12.12)
12 Electric Circuits
where L is the length of the conductor. Unit of resistivity is m.
Electrical Conductance (σ )
σ = 1/ρ
(12.5)
The units of conductance are mho/m.
Variation of Resistance and Resistivity with Temperature
R t = R 0 (1 + αT )
(12.6)
ρ t = ρ 0 (1 + αT )
(12.7)
where α is the temperature coefficient of resistance or resistivity.
Resistors in Series
R =
n
R n
(12.8)
Resistors in Parallel
1
R
=
n
1
R n
(12.9)
Joule’s law: The power (P) developed is given by
P = i
2 R = i V = V
2
/R
(12.10)
Cells
Cells in series: If n cells each of emf ξ and internal resistor r are connected in series
then the current in the circuit is given by
i =
nξ
R + nr
(12.11)
where R is the external resistance.
Cells in parallel: In this case the total emf is that of a single cell ξ . As the internal
resistances of the cells are in parallel, the equivalent internal resistance is r/n, with
the external resistance R in series. The current is
i =
ξ
R + r/n
(12.12)