Physics Classes

Category: 12th Notes

  • LC-oscillation

    LC-oscillation

    OSCILLATION IN AN LC – CIRCUIT

    LC- oscillation —-

    An LC circuit consists  an inductor and a capacitor connected in parallel . Its another name is tank circuit.

    Working –

     At t= 0 – – capacitor is first charged . The whole energy is stored in the capacitor which is U= ½ CV2 , at that instant charge on the capacitor is Q , and there is no current through the circuit and energy in the inductor at that instant is zero .

     Watch Important Physics Videos 

    At t=T/4 (T= time period of oscillation ) –  –  the capacitor begins to discharge and a  growing current starts flowing through the inductor , which setup magnetic field around it which produces induced current in the inductor  in opposite direction  and hence there is delay in discharge . As the capacitor discharges its energy starts decreasing which converted as magnetic energy in the inductor , and at an instant total charge in capacitor is zero , and hence energy stored in the capacitor is zero and energy stored in the inductor at that time is ½ LI2‑.

    At t=T/2 – as soon as capacitor is completely discharged , the magnetic field around the inductor starts decreasing , it produced an induced emf in opposite direction  , due to which capacitor start charging it self in opposite direction and at an instant inductor discharged completely and capacitor charged completely again which is ½ CV2 .

    This process repeated again and again then energy obtained once keep on oscillating between capacitor and inductor and to and fro pulses of current are produced .

    LC-OSCILLATOR
    LC-OSCILLATOR
     WORKING OF LC-OSCILLATION AND DERIVATION OF ITS FREQUENCY – Watch Video Below

    Derivation for frequency of LC- oscillation

    – Suppose an electrical circuit having a capacitor of capacitance C and an inductor of inductance L connected as shown in fog. Below-

    LC OSCILLATION
    LC OSCILLATION

    . Let the capacitor is charged Q initially and when key is closed emf induced in the inductor is L (di / dt) and potential difference across the capacitor is Q/C . Then from Kirchhoff’s law    L (dI/dt) +Q/C =0 ………..(i)

    But I = dQ /dt

    And hence eq. (i) may be written as

    L(d2Q/dt2)+ Q/C =0

    Or , d2Q/dt2 + Q/LC = 0 ………………………..(ii)

    But as we know eq . of SHM.  May be written as  d2x/dt2+ ω2x = 0  ………..(iii)

    Comparing eq. (ii) and (iii) we get

    ω2 = 1/LC

    or,  ω= 1/√LC .

    but ,   ω=2Πѵ ( where ѵ=frequency)

    so ,  frequency ,  ѵ= 1/2Π√LC

     

  • PHASOR DIAGRAM

    PHASOR DIAGRAM

    PHASOR DIAGRAM-

    PHASORS AND PHASOR DIAGRAM-

    The co-planar vectors which represents sinusoidal time varying quantities like alternating current or alternating voltage are known as phasor and the graphical representation of these quantities for the ac circuit is known as phasor diagram.

    In another words we can say when AC or alternating voltage  represented as rotating vectors in a graph is  known as phasor diagram .

    • Phasors are represented by the arrows rotating anticlockwise .
    • The length of the arrow represent the peak current or peak voltage.
    • Phasor diagram represents the phase relation between alternating current and voltage

    Representation of phasor diagram for an ac source-

    PHASOR DIAGRAM1
    PHASOR DIAGRAM-1

     

    Phasor diagram when ac circuit containing only resistance –

    PHASOR DIAGRAM -2
    PHASOR DIAGRAM -2

     Phasor diagram when ac circuit containing only capacitor-

    PHASOR DIAGRAM -3
    PHASOR DIAGRAM -3

     

    Phasor diagram when ac circuit containing only inductor-

    PHASOR DIAGRAM -4
    PHASOR DIAGRAM -4

     

  • GRAPH

    GRAPH

    GRAPH

    In this post we will discuss about the graph , and how graphs makes to understand  the physics easily ?

    Graph-

    As we know it is not easy to study or understand the physics. Students who is taking interest in physics and want to understand the physics, it is necessary to improve your mathematics and most importantly graph, students who can’t solve the graphical questions will face lot of difficulties. So I am trying to provide some information/ knowledge for the students, so that students can understand the graphical questions easily. Now these days questions based on graph is important for every topics of physics specially the students who is appearing in the JEE/ NEET examination. Graph makes the calculation easier and it makes the topic to understand more easy. So every students must have to understand the graph and solve the questions based on it.

    Pg. -1

    peg 1 graph
    peg 1 graph

    Pg. -2

    peg 2
    peg 2

    Pg. – 3

    peg 3
    peg 3

    Pg. – 4

    peg 4
    peg 4

     

     

    Pg.-5

    peg 5
    peg 5

     

  • METER-BRIDGE

    METER-BRIDGE

    METER-BRIDGE

     

    METER-BRIDGE
    METER-BRIDGE

    Question based on meter-bridge may be asked as ; What is meter-bridge ? How does it work? find the expression to find the value of unknown resistance using meter bridge.

    Meter-bridge is a devise used to know the value of unknown resistance.

     Principle -its working based on the principle of wheat-stone-bridge .

    See  the  video of complete explanation of meter bridge HERE-

    expression for unknown resistance will be given as S/R = 100-l/ l

    where R=known resistance ; S= unknown resistance ; l is the length of the uniform wire.

     

  • MUTUAL INDUCTANCE OF TWO COAXIAL SOLENOID

    MUTUAL INDUCTANCE OF TWO COAXIAL SOLENOID

    MUTUAL INDUCTANCE OF TWO COAXIAL SOLENOID

    In this topic we will derive the expression for coefficient of mutual induction or mutual inductance of two coaxial solenoid

    MUTUAL INDUCTION OF TWO COAXIAL SOLENOID–

    mutual induction
    mutual induction fig.-

    Let us consider two coaxial solenoid P1P2 and S1S2 (as shown in figure).

    Let their common length is ‘l’ with cross-sectional area  A  and having N1 turns  but second coil has N2 turns .

    If I1 is the current flows through the coil P1P2 , the magnetic field at its centre ,  B = µ0 n1 I . so magnetic flux linked with the coil S1S2 = B A .

    Magnetic flux for entire coil S1S2 , ɸ = BAN2 = µ0n1n2 A I = µ0 N1N2 I A/ l …………(i)

    But as we know , ɸ= MI ……………….(ii) (Here M is the mutual induction of the coil)

    From eq. (i) and (ii)

    MI = µ0 N1N2 I A / l

    So  M= µ0 N1N2  A/l .

     

    Points to be remember-

    • If a medium of relative permeability µr fills the entire space in the inner solenoid then mutual induction M= µ0µr N1N2  A/l
    • If the cross-sectional area of both the the coils are different then we always consider the inner coil radius ( area of that coil having smaller area of cross-section)
    • The calculation of mutual induction is quite complicated even in the case of considerable symmetry.
  • MUTUAL INDUCTION

    MUTUAL INDUCTION

    Mutual induction-

    In this topic students will study what is mutual induction and coefficient of mutual induction / mutual inductance? And what is the unit of mutual inductance

    mutual induction
    mutual induction

    Mutual induction-

    Let us consider two coils placed near to each other closely . One of the coil carries the battery is the primary coil and the other one is secondary coil connected with a galvanometer. When current starting flows through the primary coil  then its value increases from zero value to a fixed value during this time we observe that there is some deflection in the galvanometer . as we know when current passes through a coil (solenoid ) magnetic field setup ,due to increasing value of current magnetic field through the coil also increases and hence magnetic flux linked with the secondary  coil also increases , and according to Faraday’s law  emf  setup across the secondary coil .

    So we can say , The phenomena of inducing current in a circuit by changing the current in a neighbouring circuit is called mutual induction. We can also define it the property of two circuits by virtue of which each circuit opposes any change in flux or strength of current flowing through other circuit.

    It is found that the flux ‘ɸ’ linked with the secondary coil is directly proportional to the current ‘I’ flowing through the primary coil ,

    i.e.      ɸ = I

    or         ɸ = MI ( M is a constant called coefficient of mutual induction , the value of M depends upon the characteristics of the circuit ant their orientations . )

    so,     M = ɸ/I   ; if  I =1 ampere then M=ɸ

    So we can define coefficient of mutual induction is equal to the flux linked with the coil when unit current passes through the another coil.

    We know that,  emf ‘e’ = -dɸ/dt =  – d(MI)/dt  =  -M dI/dt  ,

    If dI/dt = 1 then , m  = – e , so we can define coefficient of mutual induction is equal to emf induced in secondary coil when rate of change of secondary coil is unity.

    Unit of mutual inductance  is Henry (H) , Henry is also the unit of self inductance  , we can define that mutual induction of two circuit is said to be 1 Henry if a current changing at the rate of 1 ampere per second  in one circuit and induces 1 volt of emf in other circuit.

     To derive the expression for the mutual induction of two coaxial solenoid click here

    To derive the expression for  the coefficient of self induction click here

  • Definition of Ampere

    Definition of Ampere

    Define 1 Ampere

    electric current
    electric current

    This topic only explain the term definition of Ampere ( which is explain in different-different  type . Students can learn it according to there needs.  )

    Ampere is the basic unit of electric current . It is named after Andre-Marie -Ampere a French scientist  born in 1775  . He also known as the father of electrodynamics .

    Definition of Ampere –  1 Ampere  is the current flowing through a conductor when 1 Coulomb  of charge flows through a conductors in unit time.

    From Ohm’s law – potential difference across the conductor is directly proportional to the current flowing through the conductor , if V  is the  potential difference across the conductor and I be the current flowing through the conductor then according to Ohm’s law V α I or V= RI , where R is the resistance of the conductor . ( resistance of a conductor is the property of the conductor to restrict the flow of current through it) i.e. current  I =V/R,

    So we can say, 1 Ampere current flows through a conductor when unit potential difference setup across a conductor of resistance 1 Ohm .

     

    Another definition of current can be determined using the property of force between two parallel current carrying conductor according to it force between two parallel current carrying conductor can be given as force per unit length (f/l) F= µ0I1 I2 /2Πd ( Here I1 and  I2 are the current through the wires and , d is the separation between them . according to given relation we can define, 1 Ampere is the electric current which when flowing in each of parallel conductors placed at separation  1 m in vacuum exert a force of 2x 10-7N on 1 meter length of either wire. 

     

     

     

  • ELECTRIC CURRENT

    ELECTRIC CURRENT

     ELECTRIC CURRENT or CURRENT ELECTRICITY

     

    electric- current
    electric- current

     electric current –

    Electric current –

    When electric charges is in motion , they constitute what is called an electric current . electric current is defined as the rate of flow of charge through an area of the conductor . if  Q is the charge flows through a conductor in time T then  electric current I = Q/T

    Or  I= dQ /dt . unit of current is Ampere .

    We can define 1 Ampere  is the current flowing through a conductor when 1 Coulomb  of charge flows through a conductors in unit time.

    In the terms of drift velocity current I = n e A Vd  where n is the charge density , A  is the area of cross-section of the conductor , e is the charge on electron and Vd is the drift velocity.

    In terms of Ohm’s law – current  I = V/R  V is the potential difference across the conductor and R is the resistance of the conductor .

    So we can say 1 Ampere current flows through a conductor when unit potential difference setup across a conductor of resistance 1 Ohm .

    Ampere is the basic unit of electric current . It is named after Andre-Marie -Ampere a French scientist  born in 1775  . He also known as the father of electrodynamics .

    Definition of Ampere –  1 Ampere  is the current flowing through a conductor when 1 Coulomb  of charge flows through a conductors in unit time.

    From Ohm’s law – potential difference across the conductor is directly proportional to the current flowing through the conductor , if V  is the  potential difference across the conductor and I be the current flowing through the conductor then according to Ohm’s law V α I or V= RI , where R is the resistance of the conductor . ( resistance of a conductor is the property of the conductor to restrict the flow of current through it) i.e. current  I =V/R,

    So we can say, 1 Ampere current flows through a conductor when unit potential difference setup across a conductor of resistance 1 Ohm .

     

    Another definition of current can be determined using the property of force between two parallel current carrying conductor according to it force between two parallel current carrying conductor can be given as force per unit length (f/l) F= µ0I1 I2 /2Πd ( Here I1 and  I2 are the current through the wires and , d is the separation between them . according to given relation we can define, 1 Ampere is the current which when flowing in each of parallel conductors placed at separation  1 m in vacuum exert a force of 2 x 10-7 N on 1 meter length of either wire. 

    To solve or download important objective questions of current electricity click here- Current electricity and Ohm law  objective

     

     

     

     

     

  • SELF-INDUCTION OF LONG SOLENOID

    SELF-INDUCTION OF LONG SOLENOID

    SELF-INDUCTION OF LONG SOLENOID

    self- induction
    self- induction of long solenoid

    SELF-INDUCTION OF LONG SOLENOID this topic is important for the class 12th board examination

    Self-inductance of long air-cored solenoid question may asked as –

    what do you mean by the term self-induction ? Find expression for the self-inductance of long air cored solenoid .

    Self-inductance of long air-cored solenoid –

    Suppose a long air cored solenoid having ‘n’ number of turns per unit length . If current in the solenoid is ‘I’  the magnetic field within the solenoid B= µ0nI . If A is the area of cross-section of the solenoid , the effective flux linked with the solenoid of length ‘l’ ; ɸ=NBA……………………………….(i)

    where N is the total no. of turns of the solenoid . so ɸ= n l B A …………………………………….(ii) . substituting the value of B in this equation

    we get,

    ɸ =n l(µ0nI ) A  = µ0n2A l I .

    so , self-inductance  of solenoid L=ɸ/ I.=   µ0n2A l I / I  = µ0 n2 Al

    but n= N/l

    so self- inductance L= µ0 N2A/ l .

    If solenoid contains a core of ferromagnetic material , having relative permeability µr then self-inductance  L=   µ0µr N2A/ l .

    necessary picture of this topic  is shown above**.

  • SELF-INDUCTION

    SELF-INDUCTION

    Explain the term self-induction of a coil

    Self – Induction –

    It is the property of an electric circuit or coil by virtue of which it opposes any change of flux or current in it by inducing a current in itself is called self- induction. In another words we can say “self-induction is the inertia of electricity “. Due to self -induction an electric circuit resist any change of current through it .

    As we know magnetic flux linked with a coil is directly proportional to the current flowing through the circuit

    i.e.    ɸ α I ( ɸ= flux linked with the coil, and I is the current in the circuit )

    ɸ = LI ( L is the constant called coefficient of self- induction or self-inductance  or only inductance . )

    If current I =  1 ampere, then flux ɸ= L  . so we can define self-induction is the flux linked with the coil when unit current passes through the coil.

    as we know,

    emf  e= – dɸ/dt

    e= -d (LI)/ dt

    e= -L ( dI/dt)

    L= –  e/(dI/dt)

    So we can define self-inductance of a circuit is numerically equal to the induced emf setup in it when the rate of change of current through it is unity.

    Unit of self-inductance is Henry (H) .  We can define self-inductance of a coil is one Henry if 1 volt emf induced in the coil when rate of change of current through the coil is unity.

    To find the expression for self-inductance of long solenoid click here