Electric Current (I) The rate of flow of charge through any
cross-section of a wire is called electric current flowing through it. Electric
current (I) = q / t. Its SI unit is ampere (A). The conventional direction of
electric current is the direction of motion of positive charge. The current is
the same for all cross-sections of a conductor of non-uniform cross-section.
Similar to the water flow, charge flows faster where the conductor is smaller
in cross-section and slower where the conductor is larger in cross-section, so
that charge rate remains unchanged. If a charge q revolves in a circle with
frequency f, the equivalent current, i = qf (In a metallic conductor current
flows due to motion of free electrons while in electrolytes and ionized gases
current flows due to electrons and positive ions.) Types of Electric Current
According to its magnitude and direction electric current is of two types (i)
Direct Current (DC) Its magnitude and direction do not change with time. A
ceil, battery or DC dynamo are the sources of direct current. (ii) Alternating
Current (AC) An electric current whose magnitude changes continuously and
changes its direction periodically is called alternating current. AC dynamo is
source of alternating current. Current Density The electric current flowing per
unit area of cross-section of conductor is called current density. Current
density (J) = I / A Its S1 unit is ampere metre-2 and dimensional formula is
[AT-2 ]. It is a vector quantity and its direction is in the direction of motion
positive charge or in the direction of flow of current. Thermal Velocity of
Free Electrons 2 | P a g e www.ncerthelp.com (Visit for all ncert solutions in
text and videos, CBSE syllabus, note and many more) Free electrons in a metal
move randomly with a very high speed of the order of 105 ms-1. This speed is
called thermal velocity of free electron. Average thermal velocity of free
electrons in any direction remains zero. Drift Velocity of Free Electrons When
a potential difference is applied across the ends of a conductor, the free
electrons in it move with an average velocity opposite to direction of electric
field. which is called drift velocity of free electrons. Drift velocity vd =
eEτ / m = eVτ / ml where, τ = relaxation time, e = charge on electron, E =
electric field intensity, 1 = length of the conductor, V = potential difference
across the ends of the conductor m = mass of electron. Relation between
electric current and drift velocity is given by vd = I / An e Mobility The
drift velocity of electron per unit electric field applied is mobility of
electron. Mobility of electron (μ) = vd / E Its SI unit is m2 s -1V -1 and its
dimensional formula is [M-1T 2A]. Ohm’s Law If physical conditions of a
conductor such as temperature remains unchanged, then the electric current (I)
flowing through the conductor is directly proportional to the potential
difference (V) applied across its ends. I ∝ V
or V = IR where R is the electrical resistance of the conductor and R = Ane2 τ
/ ml. Electrical Resistance 3 | P a g e www.ncerthelp.com (Visit for all ncert
solutions in text and videos, CBSE syllabus, note and many more) The
obstruction offered by any conductor in the path of flow of current is called
its electrical resistance. Electrical resistance, R = V / I Its SI unit is ohm
(Ω) and its dimensional formula is [ML2T -3A -2 ]. Electrical resistance of a
conductor R = ρl / A where, l = length of the conductor, A = cross-section area
and ρ = resistivity of the material of the conductor. Resistivity Resistivity
of a material of a conductor is given by ρ = m / n2 τ where, n = number of free
electrons per unit volume. Resistivity of a material depend on temperature and
nature of the material. It is independent of dimensions of the conductor, i.e.,
length, area of cross-section etc. Resistivity of metals increases with
increase in temperature as ρt = ρo (1 + αt) where ρo and ρt are resistivity of
metals at O°C and t°C and α temperature coefficient of resistivity of the
material. For metals α is positive, for some alloys like nichrome, manganin and
constantan, α is positive but very low. For semiconductors and insulators. α is
negative. Resistivity is low for metals, more for semiconductors and very high
alloys like nichrome, constantan etc. (In magnetic field the resistivity of
metals increases. But resistivity of ferromagnetic materials such as iron,
nickel, cobalt etc decreases in magnetic field.) Electrical Conductivity The
reciprocal of resistivity is called electrical conductivity. 4 | P a g e
www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE
syllabus, note and many more) Electrical conductivity (σ) = 1 / ρ = 1 / RA =
ne2 τ / m Its SI units is ohm-1 m -1 or mho m-1 or siemen m-1 . Relation
between current density (J) and electrical conductivity (σ) is given by J = σ E
where, E = electric field intensity. Ohmic Conductors Those conductors which
obey Ohm’s law, are called ohmic conductors e.g., all metallic conductors are
ohmic conductor. For ohmic conductors V – I graph is a straight line. Non-ohmic
Conductors Those conductors which do not obey Ohm’s law, are called non-ohmic
conductors. e.g., diode valve, triode valve, transistor , vacuum tubes etc. For
non-ohmic conductors V – I graph is not a straight line. Superconductors When
few metals are cooled, then below a certain critical temperature their
electrical resistance suddenly becomes zero. In this state, these substances
are called superconductors and this phenomena is calledsuperconductivity.
Mercury become superconductor at 4.2 K, lead at 7.25 K and niobium at 9.2 K 5 |
P a g e www.ncerthelp.com (Visit for all ncert solutions in text and videos,
CBSE syllabus, note and many more) Colour Coding of Carbon Resistors The
resistance of a carbon resistor can be calculated by the code given on it in the
form of coloured strips. Colour coding Colour Figure Black 0 Brown 1 Red 2
Orange 3 Yellow 4 Green 5 Blue 6 Violet 7 Grey 8 White 9 Tolerance power Colour
Tolerance Gold 5% Silver 10% No colour 20% This colour coding can be easily
learned in the sequence “B B ROY Great Bratain Very Good Wife”. Combination of
Resistors 1.In Series (i) Equivalent resistance, R = R1 + R2 + R3 (ii) Current
through each resistor is same. 6 | P a g e www.ncerthelp.com (Visit for all
ncert solutions in text and videos, CBSE syllabus, note and many more) (iii)
Sum of potential differences across individual resistors is equal to the
potential difference, applied by the source. 2. In Parallel Equivalent
resistance 1 / R = 1 /R1 + 1 / R2 + 1 / R3 Potential difference across each resistor
is same. Sum of electric currents flowing through individual resistors is equal
to the be electric current drawn from the source. Electric Cell An electric
cell is a device which converts chemical energy into electrical energy.
Electric cells are of two types (i) Primary Cells Primary ceUs cannot be
charged again. Voltic, Daniel and Leclanche cells are primary cells. (ii)
Secondary Cells Secondary cells can be charged again and again. Acid and alkali
accumulators are secondary cells. Electro – motive – Force (emf) of a Cell The
energy given by a cell in flowing unit positive charge throughout the circuit
completely one time, is equal to the emf of a cell. Emf of a cell (E) = W / q.
Its SI unit is volt. Terminal Potential Difference of a Cell 7 | P a g e www.ncerthelp.com
(Visit for all ncert solutions in text and videos, CBSE syllabus, note and many
more) The energy given by a cell in flowing unit positive charge through till
outer circuit one time from one terminal of the cell to the other terminal of the
cell. Terminal potential difference (V) = W / q. Its SI unit is volt. Internal
Resistance of a Cell The obstruction offered by the electrolyte of a cell in
the path of electric current is called internal resistance (r) of the cell.
Internal resistance of a cell (i) Increases with increase in concentration of
the electrolyte. (ii) Increases with increase in distance between the
electrodes. (iii) Decreases with increase in area of electrodes dipped in
electrolyte. Relation between E. V and r E = V + Ir r = (E / V – 1) R If cell
is in charging state, then E = V – Ir Grouping of Cells (i) In Series If n
cells, each of emf E and internal resistance r are connected in series to a
resistance R. then equivalent emf Eeq = E1 + E2 + …. + En = nE Equivalent
internal resistance req = r1 + r2 + …. + rn = nr Current In the circuit I = Eeq
/ (R + req) = nE / (R + nr) (ii) In Parallel If n cells. each of emf E and
internal resistance r are connected to in parallel. then equivalent emf. Eeq =
E 8 | P a g e www.ncerthelp.com (Visit for all ncert solutions in text and
videos, CBSE syllabus, note and many more) Equivalent internal resistance 1 /
req = 1 / r1 + 1 / r1 + … + 1 / rn = n / r or req = r / n Current In the
circuit I = E / (R + r / n) (iii) Mixed Grouping of Cells If n cells, each of
emf E and internal resistance r are connected in series and such m rows are
connected in parallel, then Equivalent emf, Eeq Equivalent Internal resistance
req Current in the circuit, I = nE / (R + nr / m) or I = mnE / mR + nr
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