1. Current electricity deals with flow of electric charges. Flow of
electric charges constitutes an electric current. By flow we mean of directed
motion of charges.
2. The current strength or the current through a given area of a
conductor is net charges passing per unit time through that area. Mathematically,
instantaneous electric current \[I(t) = \frac{dq}{dt}\]where dq is the charge flown through the given area in time dt. Electric
current is a scalar quantity.
3. SI unit of electric current
is 1 ampere (1 A). Current is side to be a 1 A if rate of flow of charge is 1Cs-1. As in case of metallic conductors current is mainly due to flow
of free electrons, hence in terms of electron flow 1 A electric current means
flow of 6.25 * 1018 electrons through a cross section of conductor
per second.
4. Conventional direction of electric current is the direction of
motion of positive charge. Thus, conventional current is in a direction
opposite to that of the direction of flow of electrons.
5. If current flows through a conductor at a steady rate in a given
direction, then it is called direct steady current (d.c.). However, if
direction of current remains unchanged but its magnitude varies then such a current
is called a varying current. If magnitude as well as direction change
periodically, the current is called an alternating current.
6. When current (i.e., charge) flows in a conductor, the equilibrium
distribution of charges is violated and the surface of the conductor is no
longer an equipotential surface. Thus, there is an electric field inside the
conductor and a tangential component of
electric field on the surface is also present.
7. For starting and maintaining an electric current following two
conditions should be fulfilled :(i) Sufficient number of charge carriers (free electron in metals,
ions and ionic solids and electrolytes, electrons and ions in gases, electron
and holes in semiconductors etc.) should be available. (ii) An external electric field must exist whose energy is used in
starting and maintaining the flow of charge carriers. In other words, a source
of electric energy is required.
8. To maintain a steady current, we must have a closed circuit in
which an external agency transports electric charge from lower to higher
potential energy. The work done per unit charge by the source in taking the
charge from lower to higher potential energy (i.e., from one terminal of the
source to the other) is called the electromotive force or emf to the source.
9. It should be clearly noted that the emf is not a force, it is the
potential difference between the two terminals of a source in an open circuit.
SI unit of emf is 1 volt (1 V ).
10. Positive electric charge flow from higher potential
to lower potential. External source is needed to push the charge back from
lower potential to higher potential.
11. In a conductor through which a current is flowing, Ohm’s law is
stated as “physical conditions (temperature etc.) remaining unchanged the
current flowing, through a conductor is directly proportional to the potential
difference across its ends“ i.e. $ V \propto I $ or \[V = {I}{R}\] Where R is called the resistance of given conductor.
12.Resistance of a conductor is a measure of opposition offered by it
for flow of electric current through itself. Mathematically, resistance of a given conductor is equal to the
potetial difference being maintained across its ends in order to maintain
steady flow of unit amount of current. SI unit of resistance is 1 ohm $ (1 \Omega ).$
13. The resistance of a given conductor at a given temperature is (i)
directly proportional to its length l, (ii) inversely proportional to its
cross- section area A, and (iii) depends upon the nature of the material of
conductor. Thus, \[R = \rho \frac{l}{A}\]Where p is known as the resistivity of the material of given conductor.
14. Resistivity of the material of a conductor is defined as the
resistance offered by a conductor of that material having unite length and unit
cross-section area. SI unit of resistivity is ohm- meter.For a given material, resistivity is independent of its
dimensions.
15. Reciprocal of resistance is called conductance. Thus, Conductance \[G = \frac{1}{R} = \frac{I}{V}\]SI unite of conductance is
or mho or siemen (S).
16. Reciprocal of resistivity is called the conductivity of the given
material. Thus, \[\sigma = \frac{1}{\rho} = \frac{l}{RA} = \frac{Gl}{A}\]SI unit of electric conductivity is Sm-1.
17. A perfect conductor would have zero resistivity and a perfect
insulator would have infinite resistivity. Generally, good electric conductors
are also good thermal conductors. Pure metals are good conductors having low resistivity in the
range of 10-8 -10-6 ohm m. Alloys have somewhat higher
resistivity then pure metals. Insulators like glass, rubber etc., have extremely high
resistivity ranging from 1010 m to 1016 m. The semiconductors like
germanium, silicon from a class intermediate between the conductors and
insulators. Their resistivity may vary from 10-5 m to 103m.
18. Ohm’s law is not a fundamental law of nature. Substance following
Ohm’s law have a linear V – I characteristics and are known as ohmic resistors.
Metallic conductors are ohmic resistors. Non-ohmic resistors are those, V – I characteristic for which may
have any shape other then a straight line passing through the origin. Electrolytes, semiconductor, vacuum tubes, solar cells, transistors, diodes
etc., are some examples of non-ohmic resistors. For resistors in the high range from few kilo ohms to a mega ohm,
generally, carbon resistors are used. Carbon resistors are compact, inexpensive
and, thus, find extensive use in electronic circuits.
19. For carbon resistors a colour code has been provided. According to
it, generally four bands are provided on the body of a given resistor. The
first-two bands indicate the first-two significant figure of the resistance. Third band indicate the decimal multiplier. Fourth band stands for tolerance.
| Color | Number | Multiplier | Tolerance ( % ) |
Black
| 0 | $ 10^0 $ | - |
| Brown | 1 | $ 10^1 $ | - |
| Red | 2 | $ 10^2 $ | - |
| Orange | 3 | $ 10^3 $ | - |
| Yellow | 4 | $ 10^4 $ | - |
| Green | 5 | $ 10^5 $ | - |
| Blue | 6 | $ 10^6 $ | - |
| Violet | 7 | $ 10^7 $ | - |
| Gray | 8 | $ 10^8 $ | - |
| White | 9 | $ 10^9 $ | - |
| Gold | - | $ 10^{-1} $ | 5 |
| Silver | - | $ 10^{-2} $ | 10 |
| No color | - | - | 20 |
Method to remember the color codes is " BB ROY of Great Bharat has a Very Good Wife wearing Gold Silver Necklace".
20. To understand the electric conduction in conductor, free electrons
are treated as electron gas. In the absence of an electric field, the average
velocity of free electrons is zero because their direction are random. On
applying an external electric field, the electrons move on an average with a
drift speed $ v_d $ in a direction opposite of the electric field. The
drift speed is given by \[v_d = \frac{eE}{m}\tau \implies \vec{v_d} = - \frac{e\vec{E}}{m}\tau\]Where e = electronic charge, m = mass of electron, E = external field
and τ = the average time between successive collisions of electrons
with the atoms or ions of the conductor and is knows as the relaxation period.
21. In terms of drift speed electric current is given by \[I = neAv_d \implies I = -ne(\vec{A}.\vec{v_d})\]Where n = number density of free electrons, A = normal area of
cross-section of the conductor. Direction of conventional current is opposite
to that of drift velocity of electrons.
22. Current density J is a vector
quantity and the magnitude of J is the amount of charge flowing per unit
cross-section area per second. Alternately, current per unit area ( taken
normal to the current ) is called current density. Its unit is A m-2. Current is given by \[I = \vec{J}.\vec{A}\]In terms of drift velocity,\[\vec{J} = -ne\vec{v_d}\]Here – ve sign implies that direction
of current density is opposite to that of drift velocity.
23. On the basis of the concept of dirft
speed of electron, the resistance of a conductor of length l and cross-section
area A is given by \[R = \frac{m}{ne^2\tau} \frac{l}{A}\]And the resistivity of the material of
conductor is given by \[\rho = \frac{m}{ne^2\tau}\]Thus, resistivity of the material of a
conductor is (i) inversely propositional to the number density of free
electrons, and (ii) inversely proportional to the relaxation time τ. In term of current density Ohm’s law
may be expressed as \[\vec{J} = \frac{\vec{E}}{\rho} = \sigma \vec{E}\]Where $\vec{E} $ is the external
electric field. Thus, current density $\vec{J} $ is in the direction of $\vec{E} $.
24. Magnitude of drift velocity per unit
electric field is known as the mobility. Thus, mobility\[\mu = \frac{v_d}{E} = \frac{e}{m} \tau\]The SI unit of mobility is m2/V-s.
25. For good conductors drift speed is of
the order of 10-4 -10-5 m s-1, whereas
relaxation period is of the order of 10-14s or even less.
26. The resistivity (and hence the
resistance) of all metallic conductors increase with increase in temperature.
Over a limited temperature range the relationship is linear and is given by : \[\rho_T = \rho_0[1+\alpha (T - T_0)]\]Where ρ0 is the resistivity at a reference temperature
T0 and ρT its value of temperature T. Factor a is called
the temperature coefficient of resistivity of given metal. In terms of resistance of a metallic conductor, we can write \[R_T = R_0[1+\alpha (T - T_0)]\]For elemental metals e.g., Cu, Al,
etc., value of $\alpha $ is of the order of 10-3K-1. However, for
alloy like manganin (an alloy consisting of 83% Cu, 4% Ni and 13% Mn) and
constantan (an alloy of copper and nickel) value of a is extremely small (of
the order of 10-5 K-1 ). Therefore, for preparing
standard resistor generally manganin or constantan wire is preferred. In case of insulators as well as
semiconductors the electrical resistivity decreases with increase in
temperature (or conductivity increases with increase in temperature).
27. The equivalent resistance of the
resistors in series arrangement is equal to the sum of the individual
resistance i.e., \[R_{eq} = R_1 + R_2 + R_3 +....... +R_n\]. In series arrangement same current
flows through all the resistors and potential difference across various
resister are in the ratio of individual resistances.
28. In parallel grouping of resistances
the reciprocal of the resultant (equivalent) resistance is equal to the sum of
the reciprocal of the individual resistances. i.e. \[\frac{1}{R_P} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4 }+.......\]. In parallel arrangement of resistors
potential difference across all the resistor is same but individual Currents are in the inverse ratio of
respective resistances.
29. Resistance offered by the electrolyte
of a cell is known as the internal resistance of the given cell. Internal
resistance of a cell ‘r’ depends upon
(i)
Nature and concentration of electrolyte,
(ii)
Nature of electrodes,
(iii)
Surface area of electrodes immersed into the electrolyte, and
(iv)
Separation between the electrodes.
30. Current through a resistor R when
connected to a cell of emf e and internal resistance r is given by \[I = \frac{\epsilon}{R+r}\]
31. Emf of a cell is the potential
difference between its terminals when the cell is in an open circuit i.e., when
no current is being drown from the cell. Internal resistance of the cell can be
calculated by using the formula \[r = \frac{\epsilon - V}{V}R\]
32. If a current I flows through a
conductor for time t such that potential drop across the ends of conductor be V
(or resistance of conductor be R), then amount of electric energy lost or heat
energy produced is given by \[H = I^2Rt = VIt = \frac{V^2}{R}t\]This relation is known as Joule’s law
of heating.
33. Electric power is defined as the rate
of electric energy supplied per unit time to maintain flow of electric current
through a conductor. Mathematically,\[P = VI = I^2R = \frac{V^2}{R}\] SI unit of electric power is 1 watt (1
W), where 1 watt =1 volt * 1 ampere.
34. When n cell, each of emf e and
internal resistance r, are joined in series the net emf of combination =$ n\epsilon $,
net internal resistance of combination = $ nr $ and the current flowing through an
external resistance R is given by \[I = \frac{n\epsilon}{nr + R}\]
36. If a cells of respective emfs $ \epsilon_1 , \epsilon_2 ,\epsilon_3, ...... $ and internal resistance r1, r2 …….etc.,
are joined in series such that current leaves each cell from positive
electrode, then resultant emf of combination\[\epsilon_{eq} = \epsilon_1 + \epsilon_2 +\epsilon_3 + .......+\epsilon_n\] and the internal resistance of the
combination \[r_{eq} = r_1 + r_2 + r_3 + .......+r_n\]
37. When n cells, each of emf $ \epsilon $ and
internal resistance r, are joined in parallel, the net emf of the combination = $ \epsilon $, net internal resistance of the combination = $ \frac{r}{n} $ and the current flowing
through an external resistor R is given by \[I = \frac{n\epsilon}{nR + r}\]
38. If n cells of respective emfs $ \epsilon_1 , \epsilon_2 ,\epsilon_3, ...... $ and respective internal resistance r1, r2
………. are joined in parallel, then equivalent internal resistance req
and equivalent emf eeq of the combination are given by \[\frac{1}{r_{eq}} = \frac{1}{r_1} +\frac{1}{r_2}+\frac{1}{r_3}+.........+\frac{1}{r_n}\] and \[\frac{\epsilon_{eq}}{r_{eq}} = \frac{\epsilon_1}{r_1}+\frac{\epsilon_2}{r_2}+\frac{\epsilon_3}{r_3}+...........+\frac{\epsilon_n}{r_n}\].
39. For drawing maximum power from a cell
or cell combination the total internal resistance of cell combination should be
exactly equal to the external resistance joined in the circuit.
40. To analyse complicated electrical
networks Kirchhoff gave two laws :
(i) Junction rule or current rule – the algebraic sum of all currents
flowing into a junction is zero. In the order words, at any junction, the sum
of currents entering the junction must be equal to the sum of current leaving
it. Kirchhoff’s first law of the principle of conservation of electric charge.
Mathematically, \[\Sigma I = 0\]While
applying Kirchhoff’s current rule the current flowing towards the junction is
taken + ve and the current flowing away from the junction is taken -ve
(ii) Loop rule or voltage rule – the algebraic sum of changes in
potential around any closed loop
involving resistors and cells in the loop must be zero. Mathematically, \[\Sigma V = 0 \implies \Sigma(\epsilon + RI) = 0\]Kirchhoff’s second law is based on the
principal of conservation of energy.
While applying Kirchhoff’s voltage
rule the change in potential in traversing a resistance in the direction of
current is -IR while in the opposite direction + IR. Again the change in
potential in traversing an emf source from negative to positive terminal is +e
while in the opposite direction -e.
41. A wheatstone bridge is an arrangement
of four resistances used to measure one of them in terms of other three. The
bridge is said to be balanced when the galvanometer gives null deflection. For
a balanced wheatstone bridge \[\frac{P}{Q} = \frac{R}{S}\]
Unknown resistance,S is given by\[S = \frac{Q} {P} . R\]Generally, P and Q are called the
ratio arms and R the variable arm of bridge. In a Wheatstone bridge cell and
galvanometer can be mutually interchanged without affecting the balance
condition. Moreover, resistance of diagonally opposite arms (i.e., P and S and
Q and R) may be mutually interchanged. For maximum sensitivity, all the four
resistance used in a Wheatstone bridge should be equal or nearly equal.
42. A metre bridge (also known as a slide
wire bridge) is a practical form of wheatstone bridge. It is used to find the
value of an unknown resistance X by using the formula \[X = R \frac{(100-L)}{L}\]Where R is the known resistance and L
is distance of null point from the side of resistance R.
43. A potentiometer is an extremely
sensitive and precise device to compare emfs of cells, to measure small potential difference and to measure
internal resistance of a cell. A potentiometer works on the principle
that for a constant current flowing through the potentiometer wire of uniform
cross-section the fall in potential is directly proportional to the length. While measuring an unknown potential/
emf of a cell we balance the unknown potential against an adjustable and
measuring potential difference created along the potentiometer wire.
44. The potential gradient of the potentiometer is defined as the fall in potential per unit length along the potentiometer wire. Mathematically, potential gradient k = I . σ, where I is the current flowing through the potentiometer wire and σ is the resistance per unit length of wire. For greater sensitivity potential gradient along the potentiometer wire should have a small value. This is achieved either by increasing the length of potentiometer wire or by joining a high resistance in series with the potentiometer.
45. For comparing emfs of two cells using a
potentiometer, we use the formula \[\frac{\epsilon_1}{\epsilon_2} = \frac{l_1}{l_2}\] Where l1 and l2
are the balancing length of potentiometer wire for two cells respectively.
46. A potentiometer is superior than a
voltmeter for measuring potential difference and cells because measurement is
done here in balance condition, when no current is being drawn from given cell.
47. Internal resistance of a cell ‘r’ can
also be measured by the use of a potentiometer by using the formula \[r = \frac{l_1 - l_2}{l_2} R\]Where l1 = balancing length
in open circuit of cell and l2 = balancing length when circuit of
given cell is closed through an external resistance R.
Video Lectures:
1. Electric Current, Current carriers and Drift velocity watch video
2 Mobility, Relation between current and drift velocity and ohm's law watch video
3 Resistance, resistivity and their temperature dependence watch video
4 Resistance combination watch video
5 Cells, terminal potential and grouping watch video
6 Kirchhoff's Law watch video
7 Wheatstone and meter bridge watch video
8 Potentiometer and it's application watch video
