# WBBSE Class 10 Physical Science Solutions Chapter 6 Current Electricity

Detailed explanations in West Bengal Board Class 10 Physical Science Book Solutions Chapter 6 Current Electricity offer valuable context and analysis.

## WBBSE Class 10 Physical Science Chapter 6 Question Answer – Current Electricity

Very Short Answer Type Questions :

Question 1.
What is electric current?
Electric current is general means a continuous flow of electrons, ions or any electrically charged particles through a medium.

Question 2.
What are conductors ?
The substances through which electric charge flows easily are known as conductors.

Question 3.
What are non-conductors ?
The substances which do not allow electric charge to pass through them are called non-conductors or insulators.

Question 4.
How can we define electric current in a quantitative way ?
In a quantitative way we can say that the rate of flow of electric charge through any cross section of a conductor per unit time is called the electric current.

Question 5.
What do you mean by D.C. ?
If the electric current always flow in the same direction then the current is called D.C. (Direct Current.)

Question 6.
What do you mean by A.C.?
If the direction of current alternates i.e. changes periodically from one direction to opposite direction then the current is called A.C. (Alternating current).

Question 7.
What is electric cell?
A device in which electrical energy is obtained from the chemical energy is known as electric cell.

Question 8.
What is negative electrode?
The metal rod in which there is excess of negative charge is called negative electrode of cell.

Question 9.
What is positive electrode?
The metal rod in which there is excess of positive charge is called positive electrode.

Question 10.
What is open circuit?
When the electrodes of a cell are not connected by a conductor, externally, the cell is said to be in open circuit.

Question 11.
What is close circuit?
When the electrodes are connected internally with a conductor, the cell is said to be in closed circuit.

Question 12.
What is emf of a cell?
The potential difference between the electrodes of a cell in open circuit is called emf (electromotive force).

Question 13.
What is the direction of current in the external circuit of a cell?
Current flows from positive electrode to negative electrode in the external circuit of a cell.

Question 14.
What is the emf of a simple voltaic cell?
The emf of a simple voltaic cell is 1.08 volt.

Question 15.
What is the physical nature of electromotive force?
Electromotive force is some energy.

Question 16.
What is the unit of charge in SI system?
The unit of charge in the SI system is coulomb.

Question 17.
What is the SI unit of current strength?
The SI unit of current strength is ampere.

Question 18.
What are the units of electromotive force and potential difference in SI system?
The SI unit of both electromotive force and potential difference is volt.

Question 19.
What is the SI unit of resistance?
The SI unit of resistance of Ohm.

Question 20.
State the cases in which Ohm’s law is not valid.
Ohm’s law is not valid for current flowing through gases under low pressure, electrolytes and semi-conductors.

Question 21.
How does the resistance of a conductor depend on the cross section of the conductor?
Resistance of the conductor decreases with increase of cross section.

Question 22.
In a system of resistors connected in parallel, how is the magnitude of the equivalent resistance related to the magnitude of the resistor of least value?
Equivalent resistance is smaller than the resistance of smallest resistor.

Question 23.
How is the heat generated due to electric current through a resistor related to the strength of current?
Heat is directly proportional to square of current.

Question 24.
How is the heat generated due to electric current in a resistor related to resistance of the resistor.
Heat is directly proportional to resistance.

Question 25.
What is 1 B.O.T.?
The total electric energy expended in 1 hour at the rate of 1 kilowatt is known as 1 B.O.T. (Board of Trade unit).

Question 26.
Which energy is converted to which other in an electric motor?
In an electric motor, electric energy is converted to mechanical energy.

Question 27.
What is earthing?
Earthing : It means to connect the metal case of an electrical appliance to the earth with the help of a metal wire.

Question 28.
What is the usual colour of a live wire?
The usual colour of a live wire is red.

Question 29.
What is the usual colour of a neutral wire?
The usual colour of a neutral wire is black.

Question 30.
What is the usual colour of the earthing wire?
The usual colour of the neutral wire is green.

Question 31.
Which effect of electric current is demonstrated in an electromagnet?
Magnetic effect.

Question 32.
How is current related to potential difference?
Current is directly proportional to potential difference.

Question 33.
What is the unit of resistivity in CGS system?
The unit of resistivity in CGS system is Ohm-Cm.

Question 34.
Current flows through a conductor from east to west, in which direction electrons flow through it?
Electrons flow from west to east.

Question 35.
What is an electromagnet?
An electromagnet is a temporary magnet produced by passing electtric current through an insulated copper wire coiled around a soft iron body.

Question 36.
What is the core of an electromagnet?
The soft iron body around which an insulated copper wire is coiled is called the core of the electromagnet.

Question 37.
Mention two uses of electromagnet.
Electromagnet is used in electric calling bell, electric motor.

Question 38.
What happens if the soft iron used in the electromagnet of an electric bell be replaced with steel?
The bell will not work, since the steel body turns to a permanent magnet.

Question 39.
How does the strength of an electromagnet depend on the nubmer of turns of a solenoid?
Number of turns of insulated wire per unit length of a solenoid increases strength of electromagnet.

Question 40.
What is the function of an electric switch?
Electric switch is a very common and simple device used to stop or allow flow of electric current to an electric current to an electric appliance as and when needed.

Question 41.
What is voltmeier?
A voltmeter is used to measure the potential difference between two points in a section of an electrical circuit.

Question 42.
What is an ammeter?
An ammeter is used to measure the current flowing through an electric circuit.

Question 43.
What should be the resistance of an ideal ammeter?
Ideally the resistance of ammeter should be zero.

Question 44.
What should be the reisstance of an ideal volmeter?
Ideally the resistance of voltmeter should be infinity.

Question 45.
What are the metals used to prepare fuse wire?
Usually fuses consist of fine wires made of an alloy of lead (75%) and a small amount of tin (25%).

Question 46.
What is the rating of a fuse wire?
The maximum current that may be allowed to flow through fuse wire before it melts is called the rating of fuse wire.

Question 47.
What is the nature of electric charge on an ebonite rod, when it is rubbed with cut skin?
Negative charge.

Question 48.
A glass rod is rubbed with silk. What type of charges do they acquire?
Glass is positively charged and the silk is negatively charged.

Question 49.
What is the SI unit of electric charge ?
Coulomb (C)

Question 50.
What is the least value of electric charge available?
1.6 × 10-19C

Question 51.
How many electrons will have a total charge of one coulomb?
Number of electrons = $$\frac{q}{e}$$ = $$\frac{1}{1.6 \times 10^{-19}}$$ = 6.25 × 1018.

Question 52.
Name two basic properties of electric charge.
(i) The electtric charge of an isolated system is conserved and (ii) the electric charge is quantised.

Question 53.
What is meant by conservation of charge?
It means that the total electric charge in an isolated system remains constant.

Question 54.
How is the mass of a body affected on charging?
The charging is due to transfer of electrons from one body to another. So, mass increases in the case of negatively charged body and decreases in the case of positively charged body.

Question 55.
In coulomb’s law, on what factors does the value of electrostatic force constant K depend?
It depends upon the system of units used and on the interverning medium.

Question 56.
Electrostatic force between two charges is called central force. why?
It acts along the line joining the centres of the charges, and hence, it is a central force.

Question 57.
Does a dipole experience a force, when placed in the non-uniform plectric field?
Yes, it experiences a force.

Question 58.
What is electric flux ? Write its SI unit?
The electric flux linked with a surface is the total number of lines passing through the surface. Its SI unit is Nm2 C-1.

Question 59.
What is electric potential?
The electric potential at a point is the work done in bringing a unit positive charge from infinity to that point in the electric field.

Question 60.
What is electric potential energy?
The electric potential energy is the work done in bringing charges from infinity to their respective positions to form the system.

Question 61.
Define electric potential difference between two points in an electric field.
The electric potential difference between two points in an electric field is the work done in bringing a unit positive charge from one point to the other point.

Question 62.
Illustrate a condition in which electric field is zero but potential is not zero.
Electric field inside a hollow charged sphere is zero but potential is not zero.

Question 63.
Illustrate a condition in which electric field is not zero but potential is zero.
The electric field on the equatorial line of an electrical dipole is not zero but the potential is zero.

Question 64.
Define the unit of electric unit.
The unit of current is ampere. It is the one coulomb of charge flowing through a conductor in one second.

Question 65.
What is the direction of conventional current?
It is the direction opposite to the flow of electrons in a conductor under the influence of electric field.

Question 66.
What is current density?
It is the current flowing per unit area of a conductor.

Question 67.
What is the direction of current density?
Its direction is same as that of applied electric field.

Question 68.
What is meant by steady current?
A current whose magnitude does not change with time.

Question 69.
What is meant by varying current?
A current whose magnitude changes with time.

Question 70.
What is drift velocity?
It is the average velocity with which a free-electron gets drifted in an conductor under the influence of an external electric field applied to the conductor.

Question 71.
How does the drift velocity of electrons in a metallic conductor vary with temperature?
Drift velocity of a metal decreases with increase in temperature.

Question 72.
What do you mean by relaxation time or mean free time?
It is average time interval between the two successive collisions between electron and ion in a conductor.

Question 73.
On what factors does the resistance of the conductor depend?
The resistance varies with length of the conductor and inversely proportional to area of cross section of the conductor and increases with temperature of the conductor.

Question 74.
What is the difference between Ohmic and Non-Ohmic conductors?
Ohmic conductors strictly obey Ohm’s law while Non-Ohmic conductors do not obey Ohm’s law.

Question 75.
What do you mean by conductivity of a material? Give its SI unit.
It is the reciprocal of resistivity. Its SI unit is mho m-1.

Question 76.
What is CFL ?
CFL is compact fluorescent lamp.

Question 77.
What is LED ?
LED is light emitting diode.

Question 78.
What is the value of EMF of a voltaic cell and that of a Leclanche cell ?
The value of EMF of a voltaic cell is 1.08 volt and that of Leclanche cell is 1.5 volt.

Question 79.
What is the value of permitivity of vacuum?
Its value is, ε0 = 8.854 × 10-12 C2 N-1 m-2

Question 80.
What do you mean by EMF of a cell?
EMF of a cell may be defined as the energy spent (or work done) per unit charge in taking one unit positive charge around the complete circuit.

Question 81.
What do you mean by internal resistance of a cell?
The resistance offered by a cell to the flow of current when it passes through it, is called the internal resistance of that cell. It is generally represented by r.

Question 82.
Name of metal which behaves as a superconductor?
Mercury below 4.2 K behaves as a superconductor.

Question 83.
Mention one use of superconductivity?
Superconductons are used to construct very strong magnets.

Question 84.
Which effect of current is utilized in an electric bulb?
The heating effect of current is utilized in an electric bulb.

Question 85.
Is Joule heating a reversible effect?
The phenomenon of joule heating is an irreversible one-change of the direction of current does not reverse the heating effect.

Question 86.
Why are coils of electric toasters and irons made of an alloy rather than a pure metal ?
The resistivity of an alloy is higher than the pure metal. Moreover, at higher temperature, the alloys do not melt readily. Hence, the coils of heating appliances such as electric toasters and irons are made of an alloy rather than a pure metal.

Question 87.
When an electric bulb is connected to a 12 V battery, it draws a current of 1A. What is the power of the bulb?
Power of the bulb, P = 12 V × 1 A = 12 W

Question 88.
What is the full form of EER?
The full form of EER is Energy Efficiency Ratio.

Question 89.
How can you define EER, say, for an air conditioner?
Energy Efficiency Ratio (EER) for an air conditioner can be defined as follows: EER of AC = cooling capacity (in watt)/Power Consumption (in watt)

Question 90.
Show that, potential difference × electric current = electric power
Electric power is the electric work done per unit time.
So, power P = Work done/time or, P = W/t
Putting W = V.Q = Vlt, we have, P = $$\frac{\mathrm{VIt}}{\mathrm{t}}$$ = VI
∴ Electric Power (P) = Potential difference (V) × Electric current (I).

Question 91.
Which effect of current can be utilized in detecting a current carrying wire concealed in a wall?
The electromagnetic effect can be utilized for the purpose.

Question 92.
Which rule is known as Motor rule?
Fleming’s left hand rule is known as Motor rule.

Question 93.
Who first showed that a momentary electric current is set up in closed coll of wire by moving it near a magnet or in any other magnetic field?

Question 94.
What type of energy transfer takes place in a dynamo?
A dynamo converts mechanical energy into electrical energy and generates DC.

Question 95.
Mention a way to increase the magnitude of e.m.f generated in a generator.
The magnitude of e.m.f. generated can be increased by increasing the strength of the magnetic field in the generator.

Question 96.
For a tube light, which circuit should be used?
Since a tube light consumer less power, so it should be connected to the lighting circuit (5A).

Question 97.
For an air conditioner, which circuit should be used?
Since an air conditioner consumes more power, so it must be connected to the 5 A power circuit.

Question 1.
What do you mean by potential difference?
Potential difference It is the electrical condition of a point in an electric field or on a current carrying conductor that indicates whether electrons will flow from it or it from another connected point.

Question 2.
What is the definition of coulomb ?
Coulomb : It is the quantity of electric charge that passing through silver nitrate solution deposits 0.001118 g silver at the cathode.

Question 3.
What is the definition of ampere?
Ampere : It is the current that flowing through silver nitrate solution for one second during electrolysis deposits 0.001118 g silver at the cathode.

Question 4.
What is the definition of ohm ?
Ohm : If one ampere current flowing through a conductor establishes 1 volt potential difference between the two ends of the conductor, the resistance of the conductor is one ohm.

Question 5.
State Ohm’s law.
Ohm’s law (1826) : The temperature and other physical conditions remaining constant the current flowing between any two points of a conductor is proportional to the potential difference between them.

Question 6.
Deduce the mathematical form of Ohm’s law.
Mathematical form of Ohm’s law :
Let VA and VB are the potentials at the ends A and B of the conductor A B respectively.
So, the potential difference between the points is VA – VB=V (say).

Now, if current I flows through the conductor, then following ohm’s law, V α I
or, V = R I(R= constant, the resistance of conductor )
or, $$\frac{V}{I}$$ = R

Question 7.
What is the definition of resistance from Ohm’s law ?
Definition of resistance from Ohm’s law : The resistance of a conductor is a ratio of the potential difference between its ends to the current flowing through it.

Question 8.
On what factors does the resistance of a conductor depend ?
Factors upon which the resistance of a conductor depends :
(i) Effect of length : Temperature, material and area of cross section remainning constant, the resistance (R) of a conductor is proportional to its length (1)
∴ R ∝ l (when temperature, material and cross-section are constant)
(ii) Effect of cross-section : Temperature, material and length remaining constant the resistance (R) of a conductor is inversely proportional to its area of cross-section (A)
∴ R ∝ $$\frac{1}{A}$$ (When temperature, material and length are constant)

Question 9.
What is specific resistance ?
Specific resistance : We know, R ∝ l when A is constant
R ∝ $$\frac{1}{A}$$ when l is constant
When both length and the area of cross-section of a conductor vary, then from the law of joint variation, we can write,
R ∝ $$\frac{1}{A}$$
or, R = ρ $$\frac{1}{A}$$ [ρ (rho) is the constant of proportionality and is known as the specific resistance of resistivity]
Now, if l = 1 and A = 1, then R = ρ

Definition: The specific resistance or resistivity of a material is numerically equal to the resistance of a conductor of the material of length 1 metre and area of cross-section 1 m2.

Question 10.
Specific resistance of copper 20°C is 1.6 × 10-6 ohm-cm, what do you mean by it ?
Specific resistance of copper 20°C is 1.6 × 10-6 ohm-cm}, it means: Resistance across the opposite faces of a copper cube of 1 cm side, at 20° C is 1.6 × 10-6 ohm.

Question 11.
What do you mean by combination of resistance ?
Combination of resistance : In different electrical circuit more than are resistance are connected together. This is known as combination of resistances. Usually two types of combination are used-
(i) Series combination
(ii) Parallel combination

Question 12.
Define equivalent resistance.
Equivalent resistance : The single resistance, instead of multiple resistance in a circuit, keeps the voltage and current unchanged, is called equivalent resistance of those resistances.

Question 13.
What do you mean by series combination?
Series combination: In this combination resistances are so connected that extreme end of one resistance is joined to the begining end of next resistance and so on. In this connection same current flows through all the resistances. If three resistors r1 r2 r3 connected in series, the same current I passes through each then their equivalent resistance R will be.

Question 14.
What do you mean by parallel combination?
Parallel combination : A number of resistors are said to be connected in parallel when they are placed side by side and their corresponding ends joined together so that the main current is distributed among them.

If the individual resistances is parallel combination are r1 r2 r3 then their equivalent resistance R is given by
$$\frac{1}{R}=\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}$$
So, to create a low resistance out of few relatively high resistances, those needed to be connected to parallel combination. Equivalent resistance in parallel combination is lesser than the lowest of the individual resistances.

Question 15.
What is internal resistance of a cell ?
Internal resistance: The small resistance offered by the electrolyte of a cell to the electric charges flowing through it from the negative to the positive plate is known as the internal resistance of the cell.

Question 16.
What is watt-hours ? Whose unit is it ?
Watt-hour : If an elecrtrical machine of power one watt operates for one hour then one watt hour amount of energy is said to be spent.
1 watt-hour = 1 watt × 1 hour
= 1 watt × 3600 sec = 3600 J
Unit of electrical energy is watt-hour.

Question 17.
Define 1 kilowatt-hour ?
If a machine of 1 kilo-hour operates for one hour the amount of energy spent is known as kilo-watt hour. This amount of energy is also known as Board of Trade Unit (B. O. T, units).

Question 18.
Why is nichrome wire used in electrically heated appliances ?
(i) Explanation : Nichrome, an alloy of iron (24%), nickel (60%) and chromium (16%) was much larger resistance than copper and it is about 80 times. Thus, large quantity of heat produces when electricity flows through it. It neither melts nor gets oxidized even when it is red hot. For these reasons nichrome wire is used in most of electrically heated appliances.

Question 19.
Short circuiting : It means direct connection between the two terminals of a source of electricity or through a metallic wire of feeble resistance. As a result, large current flows through the connecting wire which melts due to overheating and therefore further flow of current stops.
Overloading : It is another dangerous effect which is caused by drawing excessive current when a number of high-powered electrical appliances are simultaneously switched on.

Question 20.
What is a fuse ? What is fuse rating ?
Fuse : For the safety of the electrical gadgets one thin wire made of an alloy of lead (75 %) and tin (25%) and which has high resistance and low melting is kept in a insulator box of china clay. The thin coil is called fuse wire.
The wire is kept in series with the main circuit of the household electrical appliances.
If for some reason or other there is a surge of the current the household electical appliances may get burn. Under such condition the fuse wire melts and there by cut of the entire circuit and saves the domestic electrical equipments. Rating of fuse wire: The maximum current that may be allowed to flow through a fuse wire before it melts is called the rating of fuse wire.

Question 21.
What is earthing? How is a person saved from electric shock even if the live wire accidentally touches the metal body of an electric iron the person working with.
Earthing : It means to connect a body or the metal case of an electrical appliance to the earth with the help of a metal wire, called, earth wire.
This wire protects a person using the appliance from electric shocks.
If the live wire by chance touches the metal part of an electrical appliance which has been earthed, the current passes directly to the earth through the earth wire.

Question 22.
What is Oersted’s experiment ?
Oersted’s experiment : In this experiment, a conductor is held above and parallel to a freely rotatable pivoted magnetic needle. It is found that the magnetic needle deflects due to current flow in the conductor. The deflection increases with increase of current and it reverses when current is reversed.

Question 23.
State Ampere’s swimming rule.
Ampere’s swimming rule : If a man be imagined to be swimming along a current carrying wire in the direction of the current (south to north) with his face turned towards a freely rotating magnetic needle, then the north pole of the needle will be deflected towards his left hand.

Question 24.
State Fleming’s left hand rule.
Fleming’s left hand rule: If the thumb, the first finger and the middle finger of the left hand be held mutually perpendicular to each other in such a way that the first finger points in the direction of the magnetic field and the second finger to that of the current, then the thumb will indicate the direction at motion of the conductor.

Question 25.
Show how is Fleming’s left hand rule verified by Barlow’s wheel.
Explanation : Barlow’s wheel is an arrangement to demonstrate action of magnet on current that verifies Fleming’s left hand rule.

According to the diagram, the current carrying conductor, the toothed wheel is situated in between the magnetic poles. So, when current is allowed to flow, the wheel rotates following Fleming’s left hand rule. On reversing the current the wheel rotates in oppsoite direction following the same rule.

Question 26.
On what factors does the relocing of rotation of Barlow’s wheel depend?
Factors responsible for the speed of rotation :

1. Rotational speed increases with current and vice versa.
2. Rotational speed increases with intensity of magnetic field and vice versa.
3. If alternating current is used instead of Direct current, the wheel will try to reverse its direction with the change in direction of current resulting no rotation.

Question 27.
How can the direction of rotation of Barlow’s wheel be changed?
Factors governing the direction of rotation of Barlow’s wheel :

1. The direction of rotation will reverse if direction of current is reversed keeping direction of magnetic field unchanged.
2. The direction of rotation will reverse if direction of magnetic field is reversed keeping direction of current unchanged.
3. The direction of rotation will remain unchanged in both direction of magnetic field and direction of current are reversed.

Question 28.
A bulb is marked ‘230 V-60 W’ what does it indicate?
Explanation: When the bulb is used in an electrical line of potential difference 230 volts, 60 joules electrical Work per second is performed due to flow of electric current through the filament of the bulb.

Question 29.
What do you mean by the statement. ‘Potential difference between two points in an electric field is 5 volts’?
Explanation: ‘Potential difference between two points in an electric field is 5 volts’- this statement means an external agent has to do 5 joules work to carry 1 coulomb positive charge from a point at lower potential to a point at higher potential in the electric field.

Question 30.
Why resistivity is also called specific resistance ?
Explanation : Resistivity is also called specific resistance as resistivity of a material is the resistance offered by the material of specified dimensions unit length unit cross sectional area.

Question 31.
What is electric motor ?
Electric Motor: The device or machine which converts the electrical energy into mechanical energy is known as Electric Motor.
An insulated copper coil, wound over a suitable frame rotates in a magnetic field when electric current passes through the coil.

Question 32.
How can the strength of the motor be increased ?
The strength of an electric motor can be increased by :

1. increasing the current in the armature.
2. increasing the strength of magnetic field.
3. increasing the number of turns in the armature.

Question 33.
What is solenoid ?

Solenoid: If many turns an insulated wire wound around a cylinder the resulting coil is known as solenoid. The soft iron body around which an insulated copper wire is coiled is known as the core of the electromagnet.

Question 34.
What is electromagnet ?
Electromagnet: If soft iron is kept in a current carrying solenoid, then that soft iron behaves like a magnet so long as the current passes. This magnet is known as electromagnet.

Question 35.
How can the strength of electromagnet be increased ?
The strength of electromagnet be increased by :

1. increasing the number of turns of solenoid.
2. increasing the current through the solenoid.
3. changing the core of the electromagnet.
4. if the core is ‘U’ shaped, then the distance between the poles is minimum.

Question 36.
State a few applications of eleciromagnet in daily life.
Uses of electromagnets :

1. They are widely used in cranes for lifting and removing heavy beams etc. made of iron or steel in factories.
2. Physicians use special types of electromagent to remove small pieces of iron from the eye of a patient.
3. They are used in loudspeakers, receivers of telephone etc.

Question 37.
What is voltmeter ?
Voltmeter : A voltmeter is used to measure the potential difference between two points in a section of an electrical circuit ; the voltmeter is connected parallel to the section.

Question 38.
What is ammeter ?
Ammeter : It is used to measure the current flowing through an electric circuit where the ammeter is connected in series.

Question 39.
Why is e.m.f. (electromotive forces) of an electric cell is greater than p.d. (potential difference) ?
Explanation : The difference of potential between two poles of a cell in open circuit is e.m.f. of the cell, the potential difference between the poles in closed circuit is p.d. (potential difference) of the cell. Now, in a closed circuit, a part of the e.m.f. is expended to overcome the internal resistance of the ce: is offered by the electrolyte of the cell. So, p.d. is less than the e.m.t. cell or e.m.f. is greater than p.d.

Question 1.
What is the difference between e.m.f. and p.d. ?
Difference between e.m.f and p.d. :

 e.m.f (Electromotive Foce) p.d (Potential Difference) i. It causes conversion of some other form of energy into electrical energy. i. It causes conservation of electrical energy into some other form of energy. ii. It is the potential difference across two terminals of an open circuit cell. ii. It is the potential difference between two terminals of a closed circuit cell. iii. The magnitude of e.m.f. is greater than p.d. in a cell. iii. The magnitude of p.d. is lesser than e.m.f. in a cell. iv. It is considered as the cause of p.d. iv. Potential difference is the result/effect of e.m.f. v. It does not depend on the resistance of the circuit. v. Potential difference across any two points of a circuit depends on the resistance of that portion of the circuit.

Question 2.
State Joule’s laws of heating effect of current.
Joule’s Laws (1841) :
(i) First law : The amount of heat produced in a conductor in a given interval of time is proportional to the square of the current passed. Thus if H be the amount of heat generated in a conductor having resistance R when current I passes through it in time t, then
H ∝ P2 (when R and t are kept constant).

(ii) Second Law : The amount of heat produced by a given current in a given time is proportional of the resistance of the conductor.
H ∝ R (When I and t are kept constant)

(iii) Third Law : The amount of heat produced in a given conductor by a given current is proportional to the time for which the current passes.
H ∝ t (When I and R are kept constant)
Combining the three laws, we have
H ∝ I2 R T (when I, R and t vary)
or, H = $$\frac{I^2 R T}{\mathrm{~J}}$$
(J = mechanical equivalent of heat = 4.2 joule/calorie)
If I be in ampere, R in ohm, t in second and H in calorie, then
H = $$\frac{I^2 R T}{4 \cdot 2}$$
∴ H = 0.24 F 2 RT calorie

Question 3.
What is the difference between electromagnet and a natural or permanent magnet ?
Difference between electromagnet and natural magnet :

 Electromagnet Natural magnet i. The magnetism of this type of magnet almost disappears as soon as the current is stopped i.e. it is a temporary one. i. If properly maintained magnetism of this type of magnet is almost permanent. ii. It can be made very strong. ii. It is usually not very strong. iii. Strength of the magnet by changing the strength of the current. iii. Strength of the magnet cannot be changed. iv. By changing the number of turns per unit length of the coil, the strength of the magnet can be changed. iv. Strength of the magnet cannot be changed. v. By changing the direction of current polarity of the magnet can be easily reversed. v. In this case polarity of the magnet cannot be reversed easily.

Question 4.
An electric heater works both in A.C. and D. C. lines but Barlow’s wheel works only in D. C.- Why ?
Explanation Generation of heat in a resistor due to a current depends on magnitude of the current not on its direction. Moreover, the produced heat H ∝ I2, so even if the oppositely directed current of A.C. be taken with negative direction, on being squared, it becomes positive. So, a heater can work both in A.C. and D.C.
the rotation of Barlow’s wheel in a given magnetic field depends upon the direction of current. The direction of rotation will reverse if direction of current is reversed keeping direction of magnetic field infact.
Now, in A.C., the direction of current reverses alternately and so frequently that, as soon as Barlow’s wheel is set to rotate in one direction, the reverse current flows into it tending to rotate it oppositely. This happens continuously and very frequently, so the wheel remains static.

Numerical Problems :

Example 1:
The resistance of a conductor is 100 hm; a current of 5 ampere is flowing through it. What will be the p.d. at the two ends of the conductor?
R = 10 ohm
I = 5 ampere
V = p.d. = ?
We know,
V = RI
or, V = 10 × 5 = 50 volts

Example 2:
A current of 2A flows through a conductor. The p.d. across the conductor is 50 volts. What is the resistance?
We know,
V = R I
or, R = $$\frac{V}{I}$$ = $$\frac{50}{2}$$
I = 2 volts
R = 25 ohm

Example 3:
10 ampere current is allowed to a conductor for 1 minute. Find the amount of charge flown.
I = 10 ampere
t = 1 minute = 60 sec
Q = ?
We know,
Q = I × t
or, Q = 10 × 60 = 600
∴ Q = 600 coulomb

Example 4:
Potential difference across two points of a conductor is 60 volts. Resistance of the conductor is 10 ohm. Find the’current through the conductor.
V = 60 volts
R = 10 ohm
I = ?
We know,
V = R I
or, I = $$\frac{V}{R}$$ = $$\frac{60}{10}$$ = 6
or, I = 6 ampere

Example 5:
A current of 2 ampere is passed through a conductor of resistance 4 \mathrm{ohm}. Find the potential difference across the conductor.
I = 2 unit
R = 2 unit
V = ?
We know,
V = I × R
or, V = 2 × 4 = 8
∴ V = 8 volts

Example 6:
Resistance of one conductor is double that of the other. What will be the ratio of current through these two conductor if they are subjected to same potential difference.
Let the resistance of the conductors are R and 2 R. Let both of them are subjected to same potential difference of V. So, naturally currents in the conductors will be as follows :

Example 7:
2 units of current is flowing through a conauctor or of 2 units. What is the potential difference at the ends of the conductor?
I = 2 ampere
R = 4 ohm
V = ?
We know,
V = R . I
or, V = 2 × 2 = 4 unit

Example 8:
The resistance per metre of a wire is 1.2 ohm and its specific resistance is 60.28 × 10-8 ohm-m. Find the radius of the wire.
R = 1.2 ohm
I = 1 meter
ρ = 60.28 × 10-18ohm-m
A = ?
We know,
R = ρ $$\frac{1}{A}$$ or, A= $$\frac{\rho l}{R}$$
or, A = $$\frac{60 \cdot 28 \times 10^{-8} \times 1}{1 \cdot 2}$$
∴ A 50.2 × 10-8 m2
Again, if r be the radius of the wire,
πr2 = A = 50.2 × 10-8 or, r2=$$\frac{50 \cdot 2 \times 10^{-8}}{3 \cdot 14}$$ 16× 10-8 m2
∴ r = 4 × 10-14 m = 0.04 cm

Example 9:
There are two copper wires of equal length. The radius of one is twice the other. Find the ratio of their resistances.
r = radius of the wire
We know,

∴ The thinner wire has a resistance four times the resistance of the thicker wire.

Example 10:
The resistivity of a substance is 9 \times 10-8 \mathrm{ohm} . \mathrm{m}. What length of the wire of that material, having diameter 0.3 cm} will give a resistance of 100 \mathrm{ohm} ?
We know,

Example 11:
The resistance of wire of cross-section area 0.01 cm2 is 10 ohm. What is the length of the wire? The specific resistance of the wire is 50 × 10-6 ohm-cm.
We know,
R = 10 ohm
A = 0.01 cm2
ρ = 50 × 10-6 ohm-cm
l = ?
R = ρ $$\frac{1}{A}$$ or, l = $$\frac{RA}{\rho}$$
or, l = $$\frac{10 \times 0.01}{50 \times 10^{-6}}$$
∴ l = 2000 cm

Example 12 :
The length and area of cross-section of a wire are double of these of another wire of same material. Find the ratio of their resistances.
Let the length of wires be 2 l and l and their areas of cross. Section be 2 A and A respectively. If \rho be the resistivity of the material of the wires, then their resistance R1 and R2 will be given by
R1= $$\frac{\rho 2 l}{2 A}$$ and R2 = $$\frac{\rho l}{A}$$
∴ $$\frac{R_1}{R_2}$$ = $$\frac{1}{1}$$ or, R1 : R2 = 1 : 1

Example 13 :
Find the specific resistance of the material of a wire of length 100 cm, area of cross-section 0.2 cm2 and resistance 2 ohm.
R = 2 ohm
l = 100 cm
A = 0.2 cm2
ρ = ?
R = ρ × $$\frac{1}{A}$$
∴ ρ = $$\frac{R A}{l}$$ = $$\frac{2 \times 0.2}{100}$$ =40 ×s 10-4 ohm-cm

Example 14 :
Three resistors 1 ohm, 2 ohm and 3 ohm are connected in parallel. What will be their equivalent resistance?
We know, for parallel combination,

Example 15 :
Three wires of resistance 2 ohm, 3 ohm and 5 ohm are connected in series with a cell of e.m.f. 5 volt. What will be the current through each wire?
We know, for series combination the equivalent resistance
R = r1 + r2 + r3 = 2 + 3 + 5 = 10 ohm
We also know,
I = $$\frac{V}{R}$$ = $$\frac{5}{10}$$ = 0.5 A

Example 16 :
Find effective resistance of the resistors 2 ohm, 4 ohm, 5 ohm connected in (i) series and (ii) parallel.
We know, for series combination equivalent resistance
R = r1 + r2 + r3 = 2 + 4 + 5 = 11 ohm
We also know, for parallel combination equivalent resistance

Example 17 :
In a circuit 2 ohm and 3 ohm resistors are connected in series to the parallel arrangement of 2 ohm and 3 ohm resistors. Calculate the resistance of the circuit.
Let R be the equivalent reistance of 2 ohm and 3 ohm arranged in parallel.
So, $$\frac{1}{R}$$ = $$\frac{1}{2}$$ + $$\frac{1}{3}$$ = $$\frac{5}{6}$$
∴ $$\frac{1}{R}$$ = $$\frac{5}{6}$$ or, R = $$\frac{6}{5}$$ = 1.2 ohm
Now, 2 ohm and 3 ohm resistors are connected in series with 1.2 ohm. So, the resistance of the circuit = (2 + 3 + 1.2) ohm = 6.2 ohm.

Example 18 :
A current of 0.5 ampere passes through a wire of resistance 2.5 ohm for 1 hour. Find the heat produced.
I = 0.5 ampere
R = 2.5 ohm
t = 1 hr = 3600 sec
H = ?
We know, H = $$\frac{I^2 R T}{J}=\frac{I^2 R T}{4 \cdot 2}$$
∴ H=$$\frac{(0.5)^2 \times 2.5 \times 3600}{4.2}$$ = 535.7 calorie

Example 19 :
Two electric bulbs marked 220V-60W are used daily for 5 hours for 10 days. If the price of each unit of electrical energy be 65 paise. What will be the cost for it ?
From the problem we get, Total power of the two bulbs = 2 × 60 watt =120 watt
Electrical energy consumed per day = 120 watt × 5 hour = 600 watt-hour
∴ Total energy consumed in 10 days = 600 × 10 = 6000 watt hour
= $$\frac{6000}{1000}$$ = 6 kilo watt-hour = 6 B.O.T. unit
∴ cost of electrical energy at 65 paise per unit = 6 × 65 paise = Rs. 3.90

Example 20 :
The same current passes for the same time through two wires the resistance of one is double that of the other. What is the ratio of quantities of heat developed in the two wries?
$$\frac{H_1}{H_2}=\frac{2 R}{R}=\frac{2}{1}$$ or, H1: H2 = 2: 1