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COMPOSSED AND WRITTEN BY PROF. NAJEEB MUGHAL GOVT MUSLIM SCIENCE DEGREE COLLEGE HYD.1
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Contents:
1.
ELECTRIC CURRENT& UNIT
2.
OHMS LAW & RESISTIVITY OF MATERIAL with TEMPERATURE.
3.
COMBINATION OF RESISTORS.
4.
POWER DISSIPATION. & UNIT
5.
ELECTROMOTIVE FORCE
6.
EQUATIONS
7.
DIMENSIONS
8.
SHORT QUESTIONS AND ANSWERS.
WHAT IS ELECTRICITY?
Electricity is a form of energy. Electricity is the flow of
electrons. All matter is made up of atoms, and an atom has a center, called a nucleus. The nucleus contains
positively charged particles called protons and uncharged particles called neutrons. The nucleus of an
atom is surrounded by negatively charged particles called electrons. The negative charge of an electron is
equal to the positive charge of a proton, and the number of electrons in an atom is usually equal to the
number of protons. When the balancing force between protons and electrons is upset by an outside force,
an atom may gain or lose an electron. When electrons are "lost" from an atom, the free movement of these
electrons constitutes an electric current. Electricity is a basic part of nature and it is one of our most widely
used forms of energy. We get electricity, which is a secondary energy source, from the conversion of other
sources of energy, like coal, natural gas, oil, nuclear power and other natural sources, which are called
primary sources.
Conventional current: A flow of positive charge gives the same electric current as an opposite flow of
negative charge. Thus, opposite flows of opposite charges contribute to a single electric current. For this
reason, the polarity of the flowing charges can usually be ignored during measurements. All the flowing
charges are assumed to have positive polarity, and this flow is called Conventional current.
Direct current ( DC ): DC stands for “Direct Current,” meaning voltage or current that maintains constant
polarity or direction, respectively, over time.
Alternating current ( AC ): AC stands for “Alternating Current,” meaning voltage or current that changes
polarity or direction, respectively, over time.
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
“The rate at which charge flows through the conductor” is called electric Current.
Q
I=
t
Electric current is denoted by “” which is fundamental quantity in SI system of units
having unit “Ampere” and abs- ampere or stat –ampere in C.G.S system of unit. An
instrument used for measurement of electric current accurately is an “Ammeter”.

When one coulomb charge flows from one point to another in one second,
through a conductor, the electric current is called “One Ampere”.
I=
Q
t
ampere =
coul.
sec

“In an electrical circuit, the potential difference across the ends of a
conductor is directly proportional to the electric current passing through two
points, provided physical state of the conductor does not change.”
V 
Explanation:
Suppose electric current I is passing through a conductor by applying potential V across the
conductor. The graph plotted between them is straight line under constant resistance "R".
Mathematical derivation: Then according to the law
V 
V=R
“R” is constant, known as “Resistance” of a material. Resistance is ?the measure of
a opposition to the flow of electrical current”.
The electrical resistance of a circuit is defined as “the ratio of
the voltage applied to the electric current which flows through it”.
Its unit is “Ohm”, denoted by . The C.G.S. unit is either the abs- ohm or stat -ohm.
V
R=
I

The reciprocal of electrical resistance is called "Electrical
conductance"
1
K=
It is denoted by “K”. The unit of conductivity in SI is the Siemens also called the mho or ohm-1.
R
It is measured in Siemens.

The conductivity is the reciprocal of electrical resistivity
Electrical conductivity is also called specific conductance that is
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a measure of a material's ability to conduct an electric current.
1
Conductivity has the SI unit of Siemens per meter (S·m-1).A conductor such as


a metal has high conductivity and a low resistivity, electrical conductivity is represented
by σ.

When one Volt potential applied across the ends of the conductor
per one-Ampere electric current passing, then the resistance is called “One-Ohm”.
R=
V
I
1 ohm =
1volt
1amp.
Resistivity of a material:
 The electrical resistance of a conductor
through unit cross-sectional area per length is called "Resistivity of material".
RA
ρ=
L
Explanation:
According to the Ohm’s law, the resistance of a conductor remains constant provided length, area of crosssection and temperature do not change.
Suppose a conductor has uniform area of cross -section “A” and length “L”. It is found experimentally
that when electric current passing through it then, resistance “R” depends on these factors:
The resistance of a thicker wire is less than that of a thin one, because a thick wire has more area for the
electrons to pass through it. And the resistance to be greater and if the length is larger, since there would
be more obstacles to electron flows.
Mathematical derivation:
L
R
A
L
R=ρ
A
The “Resistivity” of a material or “specific resistance” is constant, denoted by “”. Its unit is ohmmeter. The value of Resistivity depends on the properties of material.
RA
ρ=
Hence,
L
Resistivity of the wire is large for a “bad-conductor” and it is small for the “good-conductor”.
Resistance depends on to Temperature:
 “The change in resistance per unit original resistance through unit change of temperature”, is
called temperature co-efficient of resistance, denoted by .
ΔR
α=
R o ΔT
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Explanation:
The resistance offered by a conductor, to flow of electric current is due to collision of
free electron encounter with the atoms of the lattice. As the temperature of the conductor
rises, the amplitude of the vibration of the atoms in the lattice increases and their collision
with free electrons increases. This shows that the resistance increases with the increase of
temperature.
Mathematical derivation:
Suppose a conductor has resistance “Ro” at lower temperature after heating its resistance becomes
“RT”. The change of resistance is “R” through “T” rise of temperature. It is found that,
R  Ro T
R =  Ro T
Where “” is constant known as “Temperature Co-efficient of Resistance”. Above equation can be written
ΔR
α=
as,
R o ΔT
The temperature co-efficient can be defined as,
“the fractional change in resistance per unit change of temperature”.
We get,
RT = Ro (  T + 1 )
The numbers of resistors are arranged in two different manners,
to determine equivalent resistor. One of them is known as “Parallel
combination”, while the other “Series combination”.
i) Parallel Combination:
Explanation:
Let’s suppose two resistors R1 and R2 are connected as shown. The electric current
passing through R1 and R2 is 1 and 2 respectively. The potential across both resistors is same “V” same as
the potential of battery. Such type of combination is called “Parallel
combination” of resistors.
Mathematical Derivation:
Hence,
 = 1 + 2
According to the ohm’s law, V = R1 1 , and V = R2 2
V
V
or I1 =
and, I 2 =
R1
R2
V
V
I=
+
Therefore,
R1
R2
1
1 
I = V
+

R2 
 R1
1
I
1 
= 
+
 - - - - - - ►eq. (1)
V  R1
R2 
The equivalent resistor Re has potential “V”, same as the battery potential and net electric current “” is
flowing through the network.
V = Re 
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1
I
=
Re
V
Therefore,
Put in equation1, we get,
1
1
1 
=  + 
Re
 R1 R 2 
Conclusion:

We can see from this expression that the equivalent resistance of two or more
resistors connected in parallel is always less than the least resistance in the group.
ii) Series combination:
Explanation:
Let‘s suppose two resistors R1 and R2 are connected as shown. For a series combination of resistors, the
currents in the two resistors are the same because any current that passes through R1 must also pass
through R2 and different potential difference across each resistor will be V1 and V2 respectively of network.
The sum of potential across each resistor of a circuit is equal to the V of source potential. Such type of
combination is called “Series combination” of resistors.
Mathematical Derivation:
V= V1 + V2
According to the ohm’s law, V1 =  R1 and V2 =  R2
Therefore,
V =  R 1 +  R2
V =  ( R1 + R 2 )
The equivalent resistor “Re” has potential “V” same as the battery potential and electric current “” is
passing through it.
V
=  R1 + R 2  - - - - - - ►eq (1)
I
V
Therefore,
= Re Put in equation 1,
I
We get
Re = (R1 + R2 )
Conclusion:

This relationship indicates that the equivalent resistance of a series connection of resistors is
always greater than any individual resistance.

An electric current passes through a conductor,
some useful electrical energy is dissipated in the
form of heat energy. This loss of electrical energy is due to the collision of charges with the
atoms of conductor. Loss of electrical energy in unit time is referred to as "power dissipation in
resistor".
Explanation:
Suppose charge Q passes through a resistor it losses potential energy VQ,
which shows
up heat energy. The electrical power dissipated
work
as heat is, Power =
time
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VQ
t
Mathematical derivation:
For Power Loss:
Let 'q' amount of electric charge passes through a conductor in unit time, the electric
Q
I=
current through the conductor is given by:
t
Q=I  t
Or
During the flow of electric current energy lost in the form of heat is equal to VQ, where V is the potential
difference across the ends of conductor.
Energy lost = V Q
Putting the value of Q, we get
Energy lost = V  I t 
Power =
Energy lost
=VI
t
Energy lost
= Power
t
Power = VI
Power Loss in terms of current and resistance:
According to Ohm's law V = I R. Putting the value of V, we get
Power = ( I R ) I
Power = I2R
Power Loss in terms of Resistance and Potential difference:
V
As power = V I, and according to Ohm's law, I = , putting the value of I, we get,
R
V
Power = V  
R 
V2
Power =
R
V2
Power = V I = R I 2 =
R
V2
And,
Energy dissipated = V It = R I 2 t =
t
R
The watt is the unit of measure of power. If one Coulomb charge flows through a
resister against one Volt potential difference per unit second, it is called watt.
work
VQ
Power =
=
time
t
1V
Where,
1 Watt = 1C 
1sec
Joules: A unit of electrical energy equal to the work done when a current of one ampere is passed through
a resistance of one ohm for one second.
But,
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We know that, Heat Energy = Power  Time.
One kWh = 1000 Watt  3600 Seconds
One kWh= 36105J sec-1 sec.
1 kWh = 3.6  106 J.

Eelectromotive force, emf “that which tends to cause current.” It is
the external work expended per unit of charge to produce an electric potential difference across two
open-circuited terminals
Explanation:
The electric potential difference is created by separating positive and negative charges, thereby generating
an electric field. The created electrical potential difference drives current flow if a circuit is attached to the
source of emf. When current flows, however, the voltage across the terminals of the source of emf is no
longer the open-circuit value, due to voltage drops inside the device due to its internal resistance
Suppose a source of emf “E” is connected with a resistance, say load “R”, through which uniform current
“” flows. According to the law of conservation of energy, the electrical power supplied by source “PE” must
be equal to the power dissipated “PR” in the resistor.
Therefore,
PE = PR
E  = R ²
Or
E=R
same as the Ohm’s Law
The sources of emf always have some low resistance known as “Internal resistance”, denoted by “r”.
Therefore,
PE = PR + Pr
E  = R ² + r ²
E=R+r
This shows that RI represents the Potential Difference across the resistance “R”, known as “Terminal
Potential”, denoted by Vt.
E = Vt + I r
If r = 0, then,
E = Vt
And if R = , then
=0
The kinds of sources of emf, which transform chemical energy into electrical energy, are given below,
i) Batteries or Cells convert Chemical Energy into Electrical Energy.
ii) Electrical Generators convert Mechanical Energy into Electrical Energy.
iii) Thermocouples convert Heat Energy into Electrical Energy.
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1
1
1 
=  + 
Re
 R1 R 2 
VQ
work
 Energy lost 
9. R e =  R1 + R 2  10. Power =
11. Power =
12. Power = I2 R 13. Power = 

t
time
t

V2
14. Q = n e 15. Power = V I 16. Energy lost = VQ 17. Power =
18. E = Vt + I r 19. PE = PR + Pr
R
V
t
20. E = RI 21. E = RI + rI 22. Energy lost = VI t = R I² t =
R²
1. V = R I 2 . K =
1
Q
RA
ΔR
1
3. K =
4. I= 5. ρ =
6. α =
7. R T = R o ( α ΔT + 1 )
R
T
L
R o ΔT
ρ
PHYSICAL QUANTITY & SYMBOL
I
Electric Current
Electric charge Q
Power P = VI
Energy lost VQ
Resistivity ρ =
RA
L
A
DIMENSION
[AT]
8.
UNIT
amp. = W/V = C/s
C =A sec
Watt =V·A = kg·m2·s−3
 M L T A T   A  =  M L T 
 M L2 T -2 A -1 T -1   A T    M L2 T -2  Kilo watt hour
 M L2 T -3 A -2   L2 
  M L3 T -3 A -2 
ohm.meter = kg·m3·s−3·A−2
 L
2
-2
-1
-1
2
-3
Q
[ M-1 L-2 A2 T4 ]
farad=C/V = kg−1·m−2·A2·s4
V
Electric field strength E=Voltage /meter
[M L A -1 T-3 ]
volt per metre =N/C = kg·m·A−1·s−3
Q
Electric displacement field D =
[ A T L-2]
coulomb per square metre = A·s·m−2
A
Permittivity o= Cd/A
[ M-1 L-3 A2 T4 ]
farad per metre = kg−1·m−3·A2·s4
Conductance; Admittance; Susceptance C=1/R[M−1L−2 T3 A2 ]
siemens = Ω−1 = kg−1·m−2·s3·A2
Conductivity conductance /length [M−1L−3 T3 A2 ]
siemens per meter = kg−1·m−3·s3·A2
-2
-1
Magnetic flux density, Magnetic induction B=/A [M T A ] Tesla=Wb/m2=kg·s−2·A−1=NA−1·m−1
2
-2
-1 -1
V  M L T   A T 
J C-1
=  M L2 T -3 A -2  ,
Reactance R =
= ohm ,V/A=kgm2s−3A−2=Js-1A-2=JsCoul-2
I
Amp
A
Capacitance C=
Magnetic flux  = B A
[M L2 T-2 A-1 ]
weber =V·s = kg·m2·s−2·A−1
I
[L A ]
A·m−1 = ampere per metre
L
Inductance M=potential .time/current [ML2 T-2A-2] henry=Wb/A=V·s/A= kg·m2·s−2·A−2
Permeability o = Inductance/length [M L T-2 A-2 ]
henry per metre = kg·m·s−2·A−2
Magnetic field strength H =
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Potential difference; EMF V =R I  M L2 T -2   A -1T -1  =  M L2 T -3 A -1  J C-1 = kg·m2·s−3·A−1
Q: No: 1 A charge of 3 coul. per second is passing through a conductor. What is electric current passing?
Q
Answer: I =
t
3 coul.
 =
1sec
 = 3 amp.
Q: No: 2 Define ohm and ampere.
Answer:
Ohm: One volt potential applied across the ends of a conductor through which oneampere electric current passes, the resistance of a conductor is called “One ohm”.
V
R=
I
one volt
One ohm =
one amp.
Ampere: One coulomb charge passes through conductor in one second then the electric current, is called
“one ampere”.
Q
one col.
I=
Thus , One ampere =
t
one sec.
Q: No: 3 A wire carries a charge of one coulomb in one hour. How much current flows through it?
Q
I=
Answer:
t
1coul.
I=
Therefore,  = 2.7710-4 amp.
3600 sec.
Q: No: 4 Is there any electric field inside a conductor carrying an electric current?
Answer:
Yes, there is an electric field inside a conductor carrying electric current.
Q: No: 5 What are the difficulties in testing whether the filament of a lighted bulb obeys ohm’s law?
Answer:
The filament of the bulb, say resistance, increases with the increase of temperature of a
lighted bulb. It means ohm’s law can’t obey in testing the filament of lighted bulb.
Q: No: 6 Ten resistors of different values are connected in parallel. If the potential difference across
of them is 5volts. What will be potential difference across the remaining nine resistors?
Answer:
The potential across the remaining nine resistors will also 5 volts. Because, the potential
will be same across each resistor in parallel combination,
Q: No: 7 Three resistances each of 3 ohms are to be connected to get minimum resistance .How will you
connect them? What will be minimum resistance?
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1
1
1
1
=
+
+
Re
R1 R 2
R3
Answer:
1
1 1 1
= + +
Re
3 3 3
1
3
= ,Thus Re =1 Ohm, minimum resistance.
Re
3
Three resistors are connected in parallel, to get minimum value of one ohm.
Q: No: 8 Do bends in a wire affect its resistance?
Answer:
No, there will be no any effect on resistance of a wire, when it bends.
Q: No: 9 Resistance of 10 ohm, 60 ohms and 40 ohm are connected in series .If the current is flowing
through one of them is 0.1 ampere. What is current through the other resistor?
Answer:
The current through other resistor will also 0.1 ampere. Because, the current will be same
through each resistor, when they are connected in series.
Q: No: 10 Why, does the resistance of a conductor increases with the rise of temperature?
Answer:
Because, the collisions of electrons with atoms of a conductor increase, with the increase
of temperature of a conductor. Hence, flow of electric current decreases. Thus, resistance of a conductor
increases with the rise of temperature.
Q: No: 11 Why is the resistance of a conductor is inversely proportional to the area of cross-section of a
conductor?
Answer:
A thin conductor has smaller area of cross –section, so that is difficult to flow electrons.
Hence, such conductor has larger resistance. On the other hand, a thick conductor has larger area of cross –
section, so that it is easy to flow electrons. Hence, a conductor has smaller resistance. This shows that,
1
R 
A
Q: No: 12 Why, a wire of iron has larger value of resistively than copper wire of the same size?
Answer:
Because, the value of resistively, depends on the nature of material, so that iron and
copper have different properties and different resistively.
Q: No: 13 Can you construct two wires of same length, one of copper and one of iron, that would have
same resistance at the same temperature.
Answer:
No, it is not possible that to construct two wires of same length, one of copper and one of
iron, that would have same resistance at the same temperature. Because, both wires have different
resistively.
Q: No: 14
Give the unit in which electrical powerhouse supplies energy to our houses is
measured. How this unit of energy is related to joule.
Answer:
The unit in which electrical power houses supplies energy to our houses is “Kilowatt
hour”. IKWH= 3.6106Joules
Q: No: 15 Define electric power and give its unit of measurement.
Answer:
The rate of doing work by the electrical source is called its “electric power”.
work
Power =
time
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V2
. The unit of power is Kilowatt.
R
Q: No: 16 220 volts operate 60Watt bulb. Find current passing through the filament of
bulb and energy consumed in 10 Sec..
Answer: Power =V 
Power
I=
V
60
I=
220
 = 0.2727amp.
Energy = power (time)
Energy = 60 (10)
Energy = 600 Joules
Q: No: 17 Why, is heat produced in a conductor due to flow of electric current?
Answer:
When electrons are flowing through a conductor, then opposition made by atoms of a
conductor. The flow of electrons in a wire is actually the electric current. Hence, due to the opposition,
heat produced in a conductor.
Q: No: 18
Why, is the internal resistance of a cell not constant?
Answer:
Because, the solution used in a cell is different, so that internal resistance of the cell is not
constant.
Q: No: 19 Give the unit in which electrical powerhouse supplies energy to our houses is measured.
How this unit of energy is related to joule.
Answer:
The unit in which electrical power houses supplies energy to our houses is “Kilowatt
hour”.
IKWH= 3.6106Joules
Q: No: 20 Is it possible to have a situation in which the terminal voltage will be greater than the emf of
the battery?
Answer:
We know that,
E= Vt + I r
If, r = 0 then,E = Vt . This shows that the terminal voltage never be greater than emf of the battery.
Q: No: 21 Why, a switch is connected always in series with live wire in houses and not in series with
the neutral? What will happen if the switch is placed in series with the neutral wire?
Answer:
We know that, a live wire has potential and neutral wire has zero potential. Therefore,
switch is always connected in series with the live wire to “On" and “Off”. If we replace the switch in series
with the neutral wire, then it will not be possible to stop the current flowing in a circuit.
Q: No: 22
Define electromotive force and terminal potential.
Answer: Electromotive force: The source, which maintains a steady current, known as source of emf
and the potential is called “electromotive force”.
Terminal potential: The potential at the terminals of source of emf is called ‘terminal potential”.
Q: No: 23
Name a circuit, which will give a continuously varying potential?
Answer:
The name of circuit, which will give a continuously varying potential, is "potential
divider”.
Power = V  = R 2 =
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Q: No: 24 What do you mean by complex network? Explain the terms branch, nod,
datum node and loop.
Answer: Complex Network: A circuit has number of resistors and source of potential two
or more is called “Complex network”.
Branch:
The each resistance in the complex network is called “branch”.
Node:
A single point say junction, in complex network, where number of branches is
joined is called “Node”.
Datum node: A single node point in the complex network, where maximum branches are joined, is called
“datum node”.
Loop or Mesh:
A closed circuit is called ‘loop’ or ‘mesh’.
Q: No: 25 Both potential difference and electromotive force are measured in volts. What is he difference
between these concepts?
Answer: Potential difference: It is the amount of work done in moving a unit positive charge from one
point to another in the opposite direction of electric field. Hence, Potential difference = E . d
Electromotive force: The strength of the source is called electromotive force. It is the potential difference
across terminals of the source, when it is not supplying current to an external circuit. Hence, emf = Vt + I r
Q: No: 26 What is faraday?
Answer:
One gram –atomic weight of a substance is deposited on plates will be, n e  6.021023.
Substituting the value of “charge of an electron” in coulombs, the amount of this charge comes to be
96500n coulombs. Thus, the charge transported in depositing one gram-atomic weight of a mono-valet
(n=1) ion is 96500 coulombs. This quantity of charge is called “faraday”.
Q. No: 27 It is extremely dangerous to use a plug in radio near a bathtub, when you are taking a bath.
Why? Does the same reason applying to a battery-operated radio?
Answer: Water is good conductor of electricity so that current can pass easily through water. Because,
hence it is dangerous to use a plug radio near a bathtub, when we are taking bath. The same reason
applying to battery operated radio.
Q: No: 28 What is a short circuit and open circuit means to you?
Answer:
If, the resistor connected with a battery, has negligible resistance, (R = 0) with external
circuit. It is called “short circuit”.
And if, the resistor connected with a battery, has large resistance (R =) with external circuit or in a circuit
no path to flow of current. It is called “open circuit”.
Q: No: 29 Why, is it dangerous to touch a live wire while standing on earth bare footed?
Answer:
Because, earth is a good conductor of electricity, so that electric current can easily flows,
from live wire to the earth. Hence, it is dangerous to touch a live wire while standing on earth bare footed.
Q: No: 30 You might have noticed crows sitting safely on high-tension wires. Why, are they not
electrocuted, even when sitting on a part of the wire where the insulation has worn off?
Answer:
When a crow is sitting on high-tension wire insulation is worn off, no current flows through
the crow. Because, crow is not linked with neutral wire. Thus, a crow will not be electrocuted, while sitting
on open high-tension wire.
Q: No: 31
Explain Kirchhoff’s rules?
Answer:
There are two Kirchhoff’s rules:
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Kirchhoff’s first or junction rule: At any junction point, the sum of current entering the
junction must equal to the sum of current leaving the junction.
Kirchhoff’s second or loop rule: The algebraic sum of the change in potential around any
closed path of a circuit must be zero.
Q: No: 32 Can the terminal voltage of a battery be zero?
Answer: No, it is not possible that the terminal voltage of a battery be zero.
Q: No: 33 What would you conclude from the observation that a current carrying
conductor deflects a magnetic needle placed near it?
Answer:
The deflection of the magnetic needle indicates that the current carrying conductor behaves
like a magnet.
Q: No: 34 What is the frequency of DC?
Answer:
The frequency of Direct current is Zero
Q: No: 45 Give any two points of difference between direct current and alternating current.
Answer:
Direct Current :1) It is derived from a cell or a battery and is uni-directional. 2) The positive and negative
terminals are fixed
Alternating Current :1) The current changes its direction after equal intervals of time
2) It has no fixed terminals as the current changes its direction after every half cycle. Alternating Current
Q: No: 36 Name the instrument that measures the potential difference across the ends of a current
carrying conductor. How is the instrument connected to the circuit?
Answer:
Voltmeter measures the potential difference across the ends of a conductor. It is
connected in parallel across the element through which current flows due to a certain potential difference.
Q: No: 37 Two bulbs have ratings 100 W, 220 V and 60 W, 220 V respectively. Which one has a greater
resistance?
V2
Answer:
P=
For the same V, R is inversely proportional to P. Therefore, the bulb 60 W, 220 V has
R
a greater resistance.
Q: No: 38 When are several resistors in a circuit said to be connected in parallel?
Answer:
Several resistors are said to be connected in parallel when the potential difference across the resistors
remain the same.
Q: No: 39 On what factor's does the heating effect of current depend on
Answer: The heating effect of current depends on i)The square of the amount of current flowing, ii)The
resistance of the wire and iii)The time of flow of current
Q: No: 40 Define watt and watt hour.
Answer:
Watt is the unit of power. If 1 joule of energy is consumed in 1 second, we say the
power of the device is 1 watt. Watt hour is the unit of energy. If a device with a power 1 watt works for 1
hour 1 watt hour amount of energy is consumed.
Q: No: 41 State ohm's law.
Answer:
When temperature and other physical parameters remain constant, the current flowing
through a conductor is directly proportional to the potential difference across its ends.
Q: No: 42 What is an ammeter?
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Answer: An ammeter, instrument used to measure the magnitude of an electric current
of several amperes or more
Q: No: 43 Name the factors on which the strength of electric current flowing in a given
conductor depends?
Answer: The magnitude of the electrical current flowing through a wire depends on:
1) The magnitude of the potential difference being applied to the ends of the wire. the
greater this potential difference the greater the current flow. This can be compared to a
pipe through which water is flowing. The greater the pressure differential across the length of the pipe the
greater the resulting flow.
2) The resistance of the 2wire. This depends on several characteristics of the whe wire:
A) The cross section of the wire A. Consider a wire to be like a pipe where the greater the cross section of
the pipe the greater the area through which currrent can flow. The greater the cross section, the less the
resistance, the greater the current flow.
B) The length of the wire. the longer the wire the greater the resistance, the less the current flow.
C) The resistivity of the wire. The resistivity of a wire reflects how the atomic structure of the material
affects the ease with which current can flow through the wire. A high resistivity implies that the atomic
structure inhibits the flow of current to a greater degree. Therefore, the resisance of a wire is directly
proportional to the wire's resistivity.
Q: No: 44 What's the difference between induced current and induced voltage?
Answer:
Current and voltage are two separate things. Current measures the flow of electric charge
and voltage measures the electric potential difference. Induced simply mean that there is something
causing a current or voltage (like a magnetic flux). R  L
Q: No: 45 What type of radiations is emitted by a 100 W electric bulb?
Answer:Visible light and infra-red radiations are the two types of radiations emitted by a 100 W electric
bulb.
.
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Old papers questions
Q: No: 43 Why does a short wire have less resistance And a long wire have more resistance?
Answer:
The electricity that we use is the flow of electrons through the conducting material. The loss of energy is measured in
resistance. The longer the wire, the longer the chain of atoms an electron must jump between. We know .
Q: No: 43 Is Electricity a type of energy. Or Electric current is a flow of energy.
Answer:
The above statements are wrong. Yes, electrical energy does exist. However, this energy cannot be called "Electricity,"
since Coulombs of electricity are very different from Joules of electromagnetic energy. Energy and charge are two different things,
so they cannot both be the electricity
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Electric current is the flow of charge, much like water currents are the flow of water molecules. Water
molecules tend to flow from areas of high gravitational potential energy to low gravitational potential
energy. Electric currents flow from high electric potential to low electric potential. And the
greater the difference between the high and low potential, the more current that flows!
In a majority of electric currents, the moving charges are negative electrons. However, due to historical
reasons dating back to Ben Franklin, we say that conventional current flows in the direction positive
charges would move. Although inconvenient, it's fairly easy to keep straight if you just remember that
the actual moving charges, the electrons, flow in a direction opposite that of the electric current. With this
in mind, we can state that positive current flows from high potential to low potential, even though
the charge carriers (electrons) actually flow from low to high potential.
Electric current (I) is measured in amperes (A), or amps, and can be calculated by finding the total
amount of charge ( q), in Coulombs, which passes a specific point in a given time (t). Electric current can
therefore be calculated as:
Question: A charge of 30 Coulombs passes through a 24-ohm resistor in 6.0 seconds. What is the current
through the resistor?
Answer:
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Resistance
Electrical charges can move easily in some materials (conductors) and less freely in others
(insulators), as we learned previously. We describe a material's ability to conduct electric
charge as conductivity. Good conductors have high conductivities. The conductivity of a
material depends on:
1.
2.
Density of free charges available to move
Mobility of those free charges
In similar fashion, we describe a material's ability to resist the movement of electric charge using
resistivity, symbolized with the Greek letter rho ( ). Resistivity is measured in ohm-meters, which are
represented by the Greek letter omega multiplied by meters ( •m). Both conductivity and resistivity are
properties of a material.
When an object is created out of a material, the material's tendency to conduct electricity, or
conductance, depends on the material's conductivity as well as the material's shape. For example, a
hollow cylindrical pipe has a higher conductivity of water than a cylindrical pipe filled with cotton.
However, shape of the pipe also plays a role. A very thick but short pipe can conduct lots of water, yet a
very narrow, very long pipe can't conduct as much water. Both geometry of the object and the object's
composition influence its conductance.
Focusing on an object's ability to resist the flow of electrical charge, we find that objects made of high
resistivity materials tend to impede electrical current flow and have a high resistance. Further, materials
shaped into long, thin objects also increase an object's electrical resistance. Finally, objects typically
exhibit higher resistivities at higher temperatures. We take all of these factors together to describe an
object's resistance to the flow of electrical charge. Resistance is a functional property of an object that
describes the object's ability to impede the flow of charge through it. Units of resistance are ohms ( ).
For any given temperature, we can calculate an object's electrical resistance, in ohms, using the following
formula, which can be found on your reference table.
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In this formula, R is the resistance of the object, in ohms ( ), rho ( ) is the resistivity of the material
the object is made out of, in ohm*meters ( •m), L is the length of the object, in meters, and A is the
cross-sectional area of the object, in meters squared. Note that a table of material resistivities for a
constant temperature is given to you on the reference table!
Let's try a sample problem calculating the electrical resistance of an object:
Question: A 3.50-meter length of wire with a cross-sectional
area of 3.14 × 10–6 m2 at 20° Celsius has a resistance of 0.0625
and the material it is made out of.
. Determine the resistivity of the wire
Answer:
Ohm's Law
If resistance opposes current flow, and potential difference promotes current flow, it only makes sense
that these quantities must somehow be related. George Ohm studied and quantified these relationships
for conductors and resistors in a famous formula now known as Ohm's Law:
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Ohm's Law may make more qualitative sense if we re-arrange it slightly:
Now it's easy to see that the current flowing through a conductor or resistor (in amps) is
equal to the potential difference across the object (in volts) divided by the resistance of the object (in
ohms). If you want a large current to flow, you would require a large potential difference (such as a large
battery), and/or a very small resistance.
Question: The current in a wire is 24 amperes when connected to a 1.5 volt battery. Find the resistance
of the wire.
Answer:
Note: Ohm's Law isn't truly a law of physics -- not all materials obey this relationship. It is, however, a
very useful empirical relationship that accurately describes key electrical characteristics of conductors and
resistors. One way to test if a material is ohmic (if it follows Ohm's Law) is to graph the voltage vs.
current flow through the material. If the material obeys Ohm's Law, you'll get a linear relationship, and
the slope of the line is equal to the material's resistance.
Electrical Circuits
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An electrical circuit is a closed loop path through which current can flow. An electrical
circuit can be made up of almost any materials (including humans if we're not careful!),
but practically speaking, they are typically comprised of electrical devices such as wires,
batteries, resistors, and switches. Conventional current will flow through a complete
closed-loop path (closed circuit) from high potential to low potential, therefore electrons
actually flow in the opposite direction, from low potential to high potential. If there the
path isn't a closed loop (open circuit), no charge will flow.
Electric circuits, which are three-dimensional constructs, are typically represented in two dimensions using
diagrams known as circuit schematics. These schematics are simplified, standardized representations in
which common circuit elements are represented with specific symbols, and wires connecting the elements
in the circuit are represented by lines. Basic circuit schematic symbols are shown in the Physics Reference
Table.
In order for current to flow through a circuit, you must have a source of potential difference. Typical
sources of potential difference are voltaic cells, batteries (which are just two or more cells connected
together), and power (voltage) supplies. We often times refer to voltaic cells as batteries in common
terminology. In drawing a cell or battery on a circuit schematic, remember that the longer side of the
symbol is the positive terminal.
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Electric circuits must form a complete conducting path in order for current to flow. In the
example circuit shown below left, the circuit is incomplete because the switch is open,
therefore no current will flow and the lamp will not light. In the circuit below right,
however, the switch is closed, creating a closed loop path. Current will flow and the lamp
will light up.
Note that in the picture at right, conventional current will flow from positive to negative, creating a
clockwise current path in the circuit. The actual electrons in the wire, however, are flowing in the opposite
direction, or counter-clockwise.
Voltmeters
Voltmeters are tools used to measure the potential difference between two points in a circuit. The
voltmeter is connected in parallel with the element to be measured, meaning an alternate current path
around the element to be measured and through the voltmeter is created. You have connected a
voltmeter correctly if you can remove the voltmeter from the circuit without breaking the circuit. In the
diagram at right, a voltmeter is connected to correctly measure the potential difference across the lamp.
Voltmeters have very high resistance so as to minimize the current flow through the voltmeter and the
voltmeter's impact on the circuit.
Ammeters
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Ammeters are tools used to measure the current in a circuit. The ammeter is connected in series with the
circuit, so that the current to be measured flows directly through the ammeter. The circuit must be broken
to correctly insert an ammeter. Ammeters have very low resistance to minimize the potential drop through
the ammeter and the ammeter's impact on the circuit, so inserting an ammeter into a circuit in parallel
can result in extremely high currents and may destroy the ammeter. In the diagram at right, an ammeter
is connected correctly to measure the current flowing through the circuit.
Question: In the electric circuit diagram at right, possible locations of an ammeter and a voltmeter are
indicated by circles 1, 2, 3, and 4. Where should an ammeter be located to correctly measure the total
current and where should a voltmeter be located to correctly measure the total voltage?
Answer: To measure the total current, the ammeter must be placed at position 1, as all the current in the
circuit must pass through this wire, and ammeters are always connected in series.
To measure the total voltage in the circuit, the voltmeter could be placed at either position 3 or position 4.
Voltmeters are always placed in parallel with the circuit element being analyzed, and positions 3 and 4 are
equivalent because they are connected with wires (and potential is always the same anywhere in an ideal
wire).
Energy & Power
Just like mechanical power is the rate at which mechanical energy is expended, electrical power is the rate
at which electrical energy is expended. We learned previously that when you do work on something you
change its energy, and that electrical work or energy is equal to charge times potential difference.
Therefore, we can write our equation for electrical power as:
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We also know, however, that the amount of charge moving past a point per given unit of
time is current, therefore we can continue our derivation as follows:
So electrical power expended in a circuit is the electrical current multiplied by potential difference
(voltage). Using Ohm's Law, we can expand this even further to provide us with several different methods
for calculating electrical power dissipated by a resistor:
Of course, conservation of energy still applies, so the energy used in the resistor is converted into heat (in
most cases) and light, or it can be used to do work. Let's see if we can't put this knowledge to use in a
practical application.
Question: A 110-volt toaster oven draws a current of 6 amps on its highest setting as it converted
electrical energy into thermal energy. What is the toaster's maximum power rating?
Answer:
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Another basic circuit type is the parallel circuit, in which there is more than one current path. To analyze
resistors in a series circuit, we found an equivalent resistance. We'll follow the same strategy in analyzing
resistors in parallel.
Resistors in Parallel
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Let's look at a circuit made of the same components we used in our exploration of series
circuits, but now we'll connect our components so as to provide multiple current paths,
creating a parallel circuit.
Notice that in this circuit, electricity can follow one of three different paths through each of the resistors.
In many ways, this is similar to a river branching into three different smaller rivers. Each resistor, then,
causes a potential drop (analogous to a waterfall), then the three rivers recombine before heading back to
the battery, which we can think of like a pump, raising the river to a higher potential before sending it
back on its looping path.
We can find the equivalent resistance of resistors in parallel using the formula:
Take care in using this equation, as it's easy to make errors in performing your calculations. Let's see if
we can find the equivalent resistance for our sample circuit.
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