LECTURE - 2 : CLASS VIII : SCIENCE : CHAPTER 12 : FRICTION

CLASS VIII   |    SCIENCE    |    CHAPTER 12

      Notes prepared by Subhankar Karmakar

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• FACTORS AFFECTING FRICTION:

It has been found that the friction between two surfaces depends on two factors:

(i) the nature of the two surfaces (smoothness or roughness of the two surfaces)

(ii) the force with which two surfaces are pressed together.

• 1. Dependence of friction on the nature of two surfaces:

Friction depends on the smoothness or roughness of the two surfaces which are in contact with each other. When the two surfaces in contact are smooth, then the friction between them will be small. As the degree of roughness of the two surfaces in contact increases, the friction also increases. 

• 2. Dependence of friction on the forces with which two surfaces are placed together.

The friction between two surfaces depends on the force with which the two surfaces are pressed together. Greater the weight of an object which moves over another surface, more is the force with which the two surfaces are pressed together and greater will be the friction between them. 

• Types of friction:

There are three types of friction. 

• 1. Static friction
• 2. Sliding friction and
• 3. Rolling friction

• 1. Static friction: 

The maximum frictional force present between two any two objects when one object just tends to move or slip over the surface of the other object, is called static friction. In the case of static friction, the object is actually not moving or sliding over the other object, it only takes to move or slide. It is the maximum frictional force. 

• 2. Sliding friction:

the frictional force present when one object moves slowly or slides over the surface of another object is known as sliding friction. Is the sliding friction is smaller than the static friction, it is easier to keep an object moving which is already in motion than to move the same object from rest or stationary position. Sliding friction is smaller than the static friction. 

• Why does sliding friction is smaller than the static friction?

When an object has already started moving or sliding the irregularities on its surface do not get enough time to lock into the irregularities on the surface of the other object completely. Since the interlocking of the two surfaces is less when an object has already started moving, therefore, the sliding friction is smaller than the static friction. 

• 3. Rolling friction:

when an object like a wheel rolls over the surface of another object the resistance to its motion is called rolling friction. Therefore it is always easier to roll than to slide an object over another object. Show rolling friction is much less than the sliding friction. Rolling reduces friction.

heavy machines can be easily move from one place to another by placing round logs of wood under them and then pushing with the force of hands. 

• Maximum Friction : Static Friction 
• Minimum Friction : Rolling Friction

Static friction > sliding friction > rolling friction.

Lecture-4 : CLASS-X: SCIENCE : Chapter: Electricity

CLASS X  |    SCIENCE    |    ELECTRICITY

      notes prepared by subhankar Karmakar

                                                                         

Ohm's Law: 

According to Ohm's Law, at constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends. 

If Ｉis the current flowing through a conductor and V is the potential difference (voltage) across its ends, then according to Ohm's Law:

Ｉ ∝ V  (at constant temperature)

This can also be written as:  V ∝ Ｉ

or V = RＩ

where R is a constant called "resistance" of the conductor. The value of this constant depends on the nature, length, area of cross section and temperature of the conductor. 

V/Ｉ = R

The ratio of potential difference applied between the ends of a conductor and the current flowing through it is a constant quantity called resistance.

Therefore, 

(i) The current is directly proportional to potential difference, and

(ii) The current is inversely proportional to resistance. 

a. "Current is proportional to the potential difference" - it means if the potential difference across the ends of o conductor is doubled, the current flowing through it also gets doubled, and if the the potential difference is halved the current also gets halved.

b. "The current is inversely proportional to resistance" - it means if the resistance is doubled, the current gets halved, and if the resistance is halved the current gets doubled.

Resistance of a conductor:

The property of a conductor due to which it opposes the flow of current through it is called resistance.

The resistance of a conductor depends on length, thickness, nature of material and temperature of the conductor. 

SI unit of resistance:

The SI unit of resistance is ohm. It is generated by the symbol Omega, Ω. The unit of resistance can be defined as following. "1 ohm is the resistance of a conductor such that when a potential difference of 1 volt is applied to its ends a current of 1 ampere flows through the conductor". 

Numericals on Ohm's law:

1. Potential difference between two points of a wire carrying a 0.4 ampere current is 0.6 volt. Calculate the resistance between these points.

Soln: From Ohm's law we know that resistance of a conductor is equal to the ratio of the potential difference applied across the conductor and the current flowing through it. Therefore, R = V/Ｉ

or, resistance, R = 0.6/0.4 = 3/2 = 1.5 Ω

2. A simple electric circuit has a a 12 volt battery and a resistor of 60 ohms. What will be the current in the circuit? The resistance of the connecting wires is negligible. 

Soln. From Ohm's law we know that current flowing through the circuit, Ｉ is equal to the ratio of the potential difference across the ends of the conductor V and the resistance R attached to it. 

Therefore, Ｉ = V/R = 12/60 = 0.2 A (ampere).

3. An electric appliance draws a current of 2.2 ampere from a 220 volt supply line. What current will this electric iron draw when connected to 110 volt supply line?

Soln. From Ohm's law we know that resistance of a conductor is equal to the ratio of the potential difference applied across the conductor and the current flowing through it. As the resistance of the appliance is same.

R = V₁/Ｉ₁ = V₂/Ｉ₂

V₁ = 220 V, Ｉ₁ = 2.2 A,  V₂= 110 V, Ｉ₂ = ?

Ｉ₂ =  V₂Ｉ₁/V₁ = 110x2.2 /220 = 1.1 A

4. If 20 C of charge pass a point in a circuit in two second, what is the current flowing?

Soln. Charge passing through a conductor per unit time is called current. Therefore, current, Ｉ = q/t, q = charges passing through the conductor, t = time. 

Ｉ = q/t = 20 /2 = 10 A

5. If a potential difference of 20 volt causes a current of 1 ampere to flow for 2 minute how much energy is transferred?

Soln. Q = Heat generated, Ｉ= Current = 1 A;

          R = Resistance = V/Ｉ , t = time = 120 s

Q = Ｉ²Rt = ＩVt = 1 x 20 x 120 = 2400 Joules.

LECTURE - 1 : CLASS VIII : SCIENCE : CHAPTER 12 : FRICTION

CLASS VIII   |    SCIENCE    |    CHAPTER 12

      Notes prepared by Subhankar Karmakar

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• FRICTION : 

The force which always opposes the motion of one object over another object in contact with it, is called friction. 

• friction occurs between the two surfaces which are in contact with each other. 

• friction is a force which occurs when the two objects tend to slide over each other and even when there are actually sliding over each other. 

• Direction of force of friction:

The force of friction always opposes the motion of one object over another object. The force of friction acts in a direction opposite to the direction in which an object moves. Therefore, the force of friction acts in a direction opposite to the direction of motion of an object.

• Cause of friction:

Friction is caused by the interlocking of irregularities in the surfaces of the two objects which are in contact with each other. 

When we try to move an object over the other, we have to apply a force to overcome interlocking of the irregularities in the their surfaces. More the roughness of a surface, larger is the number of irregularities on its surface and hence greater will be the friction. Thus, the force of friction is greater if very rough surfaces are involved. Friction will be less if the surface is smooth and polished. 

• Spring balance:

The spring balance is a device which is used for measuring force acting on an object. With the help of a spring balance we can measure the frictional force. 

The spring balance contains a coiled spring which gets stretched when a force is applied to its free end having a hook. The extent by which the spring gets structured is a measure of the force applied. Larger the stretching of spring, greater will be the magnitude of the force applied. the stretching of spring or magnitude of force is indicated by a pointer attached to the spring which moves on a graduated scale. The reading on the scale of spring balance give us the magnitude of force. When the spring balance is held vertically, it is used to measure the weight of an object hung from its hook. and when spring balance is held horizontally it can be used to measure the force being applied to pull the object on a horizontal surface.

• Factors affecting friction:

It has been found by experiment that friction between two surfaces depends on two factors.

• The nature of the two surfaces (smoothness or roughness of the two surfaces).
• The force with which two surfaces are pressed together.

The force of friction does not depend on the amount of surface area of the two objects which is in contact with each other. 

Dependence of friction on the nature of two surfaces:

• Friction depends on the smoothness or roughness of the two surfaces which are in contact with each other. 
• If the two contact surfaces are smooth, then the frictional force is less where as when the two contact surfaces are rough, frictional forces are more. 

LECTURE 3 : CLASS XII: PHYSICS : ELECTRIC FIELD

CLASS XII   |    PHYSICS    |    CHAPTER 1

      notes prepared by subhankar Karmakar

(the physical quantity written in bold letters are vectors )

ELECTRIC FIELD: 

The electric field or electric intensity or the electric field strength E at a point is defined as the force experienced by a unit positive test charge placed at that point, without disturbing the position of source charge. 

• Electric field E is a vector quantity. 

• SI unit of electric field is N/C. 

• Dimension of electric field is

 [E] = force/charge = [MLT⁻²]/[AT] = [MLT⁻³A⁻¹]

Electric field is an example of vector field:

As the value of electric field E is different at different point, so we can say each point having a position vector r , therefore, the vector E is a function of position vector of a point. Hence, we can say electric field is an example of vector field. 

Principle of superposition of electric fields:

It says the electric field at any point due to a group of charges is equal to the the vector sum of the electric field produced by the each charge individually at that point, when all other charges are assume to be absent. 

LECTURE 1 : CLASS XII: PHYSICS : ALTERNATING CURRENT (AC)

CLASS XII   |    PHYSICS    |    CHAPTER 1

      notes prepared by subhankar Karmakar

Alternating current:

An alternating current is that current whose magnitude changes continuously with time and direction reverses periodically. 

When a coil is rotated in a magnetic field, an alternating EMF is induced in it which is given by the relation

ℰ = ℰₒ sin (ⲱt) ---------------------------- (i)

When applied to a circuit of resistance R, it will produce a current Ｉ such that

Ｉ = ℰ/R = (ℰₒ/R) sin (ⲱt) = Ｉₒ sin (ⲱt)--------(ii)

Therefore, the current in the circuit varies sinusoidally with time and it is called alternating current. 

Ｉ = Instantaneous Current

Ｉₒ = ℰₒ/R = Maximum or peak value of current. It is also called current amplitude. 

Amplitude: The maximum value attained by an alternating current in either direction is called its amplitude or peak value and is denoted by Ｉₒ. 

Time Period: The time taken by an alternating current to complete one cycle of its variations is called its time period and is denoted by T.

This time is equal to the time taken by the coil to complete one rotation in the magnetic field. 

T = 2π/ⲱ ; where ⲱ = angular velocity of the coil. 

Frequency: The number of cycles completed per second by an alternating current is called its frequency and is denoted by f. It is equal to the frequency of rotation of the coil in the magnetic field. 

f = 1/T = ⲱ/(2π)

∴ Ｉ = Ｉₒ sin (ⲱt) = Ｉₒ sin (2πft) = Ｉₒ sin (2πt/T) -------- (iii)

• In India AC supply has a frequency of 50 Hz

Mean / Average Value of AC over a half cycle:

Average value of AC : It is defined as that value of direct current which sends the same charge in a circuit in the same time as is sent by the given alternating current in its half time period. It is denoted by Ｉₘ or Ｉₐᵥ.

LECTURE 2 : CLASS XII: PHYSICS : ELECTRIC CHARGE & FIELD NUMERICALS

CLASS XII   |    PHYSICS    |    CHAPTER 1

      notes prepared by subhankar Karmakar

Numericals on quantization of charge:

1. Which is bigger 1 coulomb or a charge on an electron? How many electronic charges form one coulomb of charge?

2. If a body gives out 10⁹ electrons every second, how much time is required to get a total charge of 1 coulomb from it?

3. How much positive and negative charge is there in a cup of water? (Take the mass of water contained in a cup is 250 g).

4. Calculate the charge carried by 12.5 x 10⁸ electrons. 

5. Estimate the total number of electrons present in hundred gram of water. How much is the total negative charge carried by these electrons? (Take Avogadro number = 6.02 x 10²³ and molecular mass of water = 18).

Numericals on Coulomb's law of electrostatics:

6. Two particles, each having a mass of 5 gram and charge 0.1 microcoulomb , stay in limiting equilibrium on a horizontal table with a separation of 10 centimetre between them. The coefficient of friction between each particle and the table is same. Find the coefficient of friction.

7. Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 x 10⁻⁷ C ? The radii of A and B are negligible compared to the distance of separation. What will be the force of repulsion if the two spheres are placed in water?

8. Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally remove from both. What is the new force of repulsion between A and B?

9. Two similarly equally charged identical metal spheres A and B repel each other with a force of 2.0 x 10⁻⁵ N. A third identical unchaged sphere C is touched to A, then placed at the mid point between A and B. Calculate the net electrostatic force on C. 

10. Two identical charges, Q each, are kept at a distance r from each other. A third charge q is placed on the line joining the above two charges such that all the three charges are in equilibrium. What is the magnitude, sign and position of the charge q?

Numericals on the superposition principle:

11. Consider three charges q₁, q₂, q₃ each equal to q at the verices of an equilateral triangle of side l. What is the force on a charge Q placed at the centroid of the triangle?

12. Consider the charges +q, +q and -q placed at the vertices of an equilateral triangle. What is the force on a charge?

13. Four equal point charges each 16 μC are placed on the four corners of a square of side 0.2 m. Calculate the force on any one of the charges. 

1 mark questions:

1. Two identical metallic spheres of exactly equal masses are taken. One is given a positive charge q and other an equal negative charge. Are their masses after charging equal?

2. Can two like charges attract each other? If yes, how?

3. Electrostatic experiments do not work well on humid days.  give reasons. 

4. A comb runs through one's dry hair attract small bits of paper. Why? What happens if the hair is wet or if it is a rainy day?

5. Ordinary rubber is an insulator. But the special rubber tyres of aircrafts are made slightly conducting. Why is this necessary?

6. Vehicles carrying inflammable materials is usually have metallic ropes touching the ground during motion. Why?

7. An inflated balloon is charged by rubbing with fur. Will it stick readily to a conducting wall or to an insulating wall? Give reason.

8. What does q₁ + q₂ = 0 signify in electrostatics?

9. Can a body have a charge of 2.4 x 10⁻¹⁹ C? Justify your answer by comment?

10. If the distance between two equal point charges is doubled and their individual charges are also doubled, what would happen to the force between them?

MOVING COIL GALVANOMETER

Galvanometer: 

A galvanometer is a device to detect current in a circuit. 

Principle: 

A current carrying coil placed in a magnetic field experiences a current dependent torque, which tends to rotate the coil and produces angular deflection. 

Construction:

A galvanometer consists f a rectangular coil of fine insulated copper wire wound on a light non magnetic metallic frame. The two ends of the axle of this frame are pivoted between two bearings. The motion of the coil is controlled by a pair of hair springs of phosphor bronze. The inner ends of the springs are soldered to the two ends of the coil and the outer ends are connected to the the binding screws. The springs provide the restoring torque and serve as current leads. A light aluminium pointer attached to the coil measures its deflection on a suitable scale. 

The coil is symmetrically placed between the cylindrical pole pieces of strong permanent horseshoe magnet. 

Theory and Working:

Let Ｉ = current flowing through the coil PQRS

     a, b = sides of the coil PQRS

       A  = ab = area of the coil

       θ = angle between the direction of B and normal to the plane of the coil.

       N = number of turns in the coil

Since the field is radial, the plane of the coil always remains parallel to the field B. Magnetic forces on the sides QR and SP are equal, opposite and collinear, so their resultant is zero. According to Fleming's left hand rule, the side PQ experiences a normal inward force equal to NＩbB why is the side QR experiences an equal normal out what force. The two forces on sides PQ and RS are equal and opposite. They form a couple and exert a torque given by 

τ = one of the force x perpendicular distance between them 

τ = F a sin θ = ＩbBa sin θ = ＩBA sin θ

[ ∵ ab = A]

If the rectangular loop has N turns, the torque increases N times ie.,

τ = NＩBA sin 90° = NＩBA

Here, θ = 90°, because the normal to the plane of coil remains perpendicular to the field B in all positions. 

The torque τ deflects the coil through an angle α. A restoring torque is set up in the coil due to elasticity of the springs such that

      τᵣ ∝ α   or   τᵣ = kα 

Where K is is the the torsion constant of the springs. 

Restoring Torque = Deflecting Torque

kα = NＩBA

Or  α = (NBA/k)Ｉ

Or      α ∝ Ｉ

Thus the deflection produced in the galvanometer coil is proportional to the current flowing through it. Consequently, the instrument can be provided with a scale with equal divisions along a circular scale to indicate equal steps in current. Such a scale is called linear scale.

Ｉ = (k/NBA) α = Ｉ = Gα

G = (k/NBA) is constant for a galvanometer and is called galvanometer constant for current reduction factor of the galvanometer.