Mirror numerical

 Problem 1

Problem: A concave mirror has a focal length of 15 cm. An object is placed 30 cm in front of the mirror. Find the position of the image.

So, the image is formed 30 cm in front of the mirror.

Problem 2

Problem: A concave mirror has a focal length of 10 cm. An object is placed 25 cm in front of the mirror. Determine the position and nature of image.

So, the image is formed approximately 16.67 cm in front of the mirror. The negative sign indicates the image is real and inverted.

Problem 3

Problem: An object 5 cm tall is placed 20 cm in front of a concave mirror with a focal length of 10 cm. Find the position, size, and nature of image.

Numerical Problem[electricity]

Solve these numericals and comment your answer dear students...

Question 1
A wire of length 3 m and area of cross-section 1.7 × 10^-6 m² has a resistance 3 × 10^-2 ohm.


Question 2
We have four resistors A ,B ,C and D of resistance 4 ohm,8 ohm ,12 ohm and 24 ohm respectively?

Question 3
A 4Ω resistance wire is doubled on it. Calculate the new resistance of the wire.
Question 10.

Question 4
A student has a resistance wire of 1 ohm. If the length of this wire is 50 cm, to what length he should stretch it uniformly so as to obtain a wire of 4 Ω resistance? Justify your answer.
  
Question 5.
Calculate the resistivity of the material of a wire of length 1 m, radius 0.01 cm and of resistance 20 ohms.
   
Question 6
 Three resistors of 1 Ω, 2 Ω and 3 Ω are connected in parallel in a circuit. If 1 Ω resistor draw a current of 1 A, find the current through the other two resistors.

Question 7
Establish a relationship to determine the equivalent resistance R of a combination of three resistors having resistance R₁, R₂ and R₃ connected in series.

[1]- Calculate the equivalent resistance of the combination of three resistors of 2 Ω, 3 Ω and 6 Ω joined in parallel.

Question 8
Calculate the amount of work done in shifting a charge of 2 coulombs from a point A to B having potentials 10 V and 5V respectively.

 Question 9
What would be the resistance of a resistor if the current flowing through it is 0.15 A when the potential difference across it is 1.05 V?
  
Question 10
A copper wire has a diameter 0.5 mm and resistivity 1.6  10^-8ohm m.
(i) What will be the length of this wire to make the resistance of 12 Ohm.

(ii) How much will be the resistance of another copper wire of same length but half the diameter?

Question 11
A wire of uniform cross-section and length l has a resistance of 4 ohm. The wire is cut into four equal pieces. each piece is then stretched to length ‘l’. Thereafter, the four wires are joined in parallel. Calculate the net resistance.

Question 12
Calculate the electrical energy produced in 5 minutes when a current of 2 A is sent through a conductor by a potential difference of 500 volts.

Question 13
An electric bulb draws a current of 0.2 A when it operates at 220 V. Calculate the amount of electric charge flowing through it in 1 h.

Question 14
Resistors are given as R₁ = 10 ohm, R₂ = 20 ohm, and R₃ = 30 ohm. Calculate the effective resistance when they are connected in series. Also calculate the current flowing when the combination is connected to a 6 V battery.

Question 15
The filament of an electric lamp, which draws a current of 0.2 A, is used for 5 hours. Calculate the amount of charge flowing through the circuit.

Resistance[ class- 10]

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Resistance

Definition: It is the opposition force experienced by the flowing electrons in some substances.

This opposes the flow of electricity in a material.

The SI unit of resistance is represented by a greek symbol Ω

The resistance symbol of a resistor is given below.

Resistance Formula

The resistance formula is as follows:

Resistance = voltage drop across a resistor/ current flowing through a resistor

                         [ R = $\frac{V}{I}$]
R = resistance (Ohms, Ω)
V = voltage difference which is between the two ends of a resiistance.

RESISTANCE DIPENDS ON FOLLOWING FACTOR---

[1]- Resistance is directly proportional to the length of the material”.

 According to this law, the resistance of the material increases with the increase in the length of the material and decreases with the decrease in the length of the material.

                 [ R ∝ L ]—–------(1)

[2]-Resistance is inversely proportional to the cross-sectional area of the material”. 

According to this law, its material increases with the decrease in the cross-sectional area of the conductor and decreases with an increase in the cross-sectional area.

                     [ R ∝ 1/A ]—------(2).

[3]-Resistance depends on the nature of the material”.

According to this law, the resistance value of the material varies depending upon the type of material.

[4]-Resistance depends on its temperature”. According to this law when the temperature of a metallic conductor is increased, it’s value also increases.

From equation first and second--

               [ R = ρL/A]

where ρ is known as the resistivity constant or the coefficient of resistance.

Note-It is also known as the specific resistance of the material. Its units are Ohm-meter

Ohm's Law[class-10]

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Ohm's Law

According to the Ohm's law, "The electric current flowing through a conductor is directly proportional to the potential difference across its ends provided the physical conditions (temperature, dimensions, pressure) of the conductor remains the same."

Ohm’s Law Formula

[Voltage= Current× Resistance]

                             [V= I×RV]
where, v= voltage, I= current and  R= resistance
NOTE-In other words by doubling the voltage across a circuit the current will also double.
However if the resistance is doubled the current will fall by half.

In this mathematical relationship the unit of resistance is measured in Ohms.

Limitations of Ohm’s Law

• [1]-Ohm’s law is not applicable in unilateral networks. Unilateral networks allow the current to flow in one direction. 
• Such types of network consist elements like a diode, transistor, etc.
• 
  
• [2]-It is not applicable for the non-linear network. In the nonlinear network, the parameter of the network is varied with the voltage and current.
• 
  
• [3]-Their parameter likes resistance, inductance, capacitance and frequency, etc., not remain constant with the times.
• So ohms law is not applicable to the nonlinear network.

NOTE-Ohm’s law are used for finding the resistance of the circuit and also for knowing the voltage and current of the circuit.

Question related to charge,current and potential difference[class=10]

Electric Current and Circuit

Q.1 What is electric charge?

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges: positive and negative.

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Q.2 Describe the properties of electric charges?

Properties : -

(a) Opposite charges (or unlike charges) attract each other.

(b) Similar charge (or like charges) repel each other.

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Q.3 What do you mean by static electricity and current electricity?

Static electricity is an imbalance of electric charges within or on the surface of a material. The charge remains until it is able to move away by means of an electric current or electrical discharge.

Current electricity is the set of physical phenomena associated with the presence and flow of electric charge.

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Q.4 What do you mean by electric current?

The electric current is a flow of electric charges (called electrons or protons) in a conductor such as a metal wire.

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Q.5 What is the S.I. unit of electric charge and current?

S.I. unit of

Charge – Coulomb

Current – Ampere

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Q.6 State  the basic differences between conductor and insulator.

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Q.8 Calculate the number of electrons constituting one coulomb of charge? (Charge on one electron = 1.6 × 10-19C)

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Q.10 How is an ammeter connected in a circuit to measure current flowing through it?

An ammeter is connected in series in a circuit to measure current flowing through it.

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Q.11 In an electric circuit, state the relationship between the direction of conventional current and the direction of flow of electrons?

The direction of conventional current is opposite to the direction of flow of electrons.

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Q.12 What does an electric circuit mean? Distinguish between an open and a closed circuit?

A continuous and closed path of electric current is called electric circuit.

In an open circuit, the switch key is open. While in a closed circuit, the switch key is closed.

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Q.13 Define electric current with its S.I. unit. Write its formula:

Electric Current is the amount of charge flowing through a particular area in unit time.

SI unit of current I = Ampere

Formula = I = Q / t = Coulomb/time

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Q.14 The amount of charge passing through a cell in four seconds in 12 C. Find the current supplied by cell.

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Q.15 Calculate the number of electrons that could flow per second through the cross section of a wire when 4 A current flows in it.

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Q.16 A current of 10 A flows through a conductor for two minutes :

(a) Calculate the amount of charge passed through unit area of cross section of the conductor.

(b) If the charge of an electron is 1.6 × 10-19 C then calculate the total number of electrons flowing.

Q.17    What is the SI unit of charge? Is it a scalar or vector quantity?

SI unit of charge is coulomb (C) = It is scalar quantity

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Q.18 Define 1 C or one coulomb?

1 C charge is the charge which when placed at a distance of 1 m from an equal like charge in vacuum, experiences a repulsive force on 1 N.

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Q.19 Define 1 A or one Ampere?

When 1 coulomb of charge flows through any cross-section of a conductor in 1 sec., the electric current flowing through it is said to be 1 ampere i.e.

1 ampere = 1 coulomb/ 1 second

Or 1 A = 1 C/1 s

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Q.20 Write down the formula which relates electric charges,time and electric current ?

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Q.21 By what name is the physical quantity coulombs / second called ?

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Q.23    What are the fundamental laws of Electrostatics?

Fundamental laws of electrostatics –

(a) There are two types of charges – one is positive and other is negative.

(b) Like charge repel each other and unlike charges attract each other.

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Q.25 Name a device that helps to maintain a potential difference across a conductor.

Cell, battery, power supply etc. are the devices that help to maintain a potential difference across a conductor.

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Q.26 A current of 0.75 A is drawn by a filament of an electric bulb for 5 minutes. Find the amount of electric charge that flows through the circuit.

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Q.27 Why does an ammeter burn out when connected in parallel in an electric circuit?

An ammeter is a low Resistance device. So, it should always be connected in series to a circuit for measuring current effectively. 

However, if it is connected in parallel, the resistance of the circuit reduces considerably and a large amount of current flows through the circuit which may lead to the burning of the ammeter.

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Q.28 Name the instrument used to change the resistance of the circuit?

Rheostat is the instrument used to change the resistance of the circuit.   

Physics Class 9[Motion] PArt=2

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5. acceleration

• Acceleration is a measure of the change in the velocity of an object per unit time. 
  
• If the velocity of an object changes from an initial value u to the final value v in time t, the acceleration a is given by,
• 
  $a=\frac{v-u}{t}$
  .
•  Uniform Acceleration =If it travels in a straight line and its velocity increases by equal amount in equal intervals of time. 
• Example =freely falling bodies, motion of ball rolling down the inclined plane etc.
• 
  
•  Non Uniform Acceleration =If its velocity increases or decreases by unequal amount in equal intervals of time.
• 
  
• If acceleration is in the direction of the velocity then it is positive acceleration.
•  
• If it is in the direction opposite to the direction of velocity then it is negative and the negative acceleration is termed retardation.
• 
  
• SI unit of acceleration is ms^-2.

Concept Map of Acceleration

Fill in the blanks
1.Speed
2. SI
3. time
4. Velocity
5. Displacement
6. direction
7. Motion
8. Direction
True and False Statement
1. False
2. True
3. True
4. True
5. false
6. false
7. false

6. Equations of uniformly accelerated motion

• There are three equations of bodies moving with uniform acceleration which we can use to solve problems of motion==

First Equation of motion

• The first equation of motion is $v=u+at$ ,
•  Where= v is the final velocity 
•     u is the initial velocity of the body.
• 
  
• NOTE--First equation of motion gives velocity acquired by body at any time $t$.
• 
  
• Now we know that acceleration
  

Second Equation of motion

• Second equation of motion is
  $s=ut+\frac{1}{2}a{t}^2$
• 
  

Where =$u$ is initial velocity, 
• $a$ is uniform acceleration 
•  $s$ is the distance traveled by body in time $t$.
• 
  
• NOTE=Second equation of motion gives distance traveled by a moving body in time $t$.

Third equation of motion

• Third equation of motion is
  $v^2=u^2+2as$
• 
  
Where= $u$ is initial velocity,
•  $v$ is the final velocity,
•        $a$ is uniform acceleration    
•  $s$ is the distance travelled by the body.
• 
  
• NOTE=This equation gives the velocity acquired by the body in traveling a distance $s$.
• 
  
• These three equations of motion are used to solve uniformly accelerated motion problems and following three important points should be remembered while solving problems.
• 
  
  1. if a body starts moving from rest its initial velocity $u=0$
  2. if a body comes to rest i.e., it stops then its final velocity would be $v=0$
  3. If a body moves with uniform velocity then its acceleration would be zero.