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List of Important Derivations: (XII) (1) Electrostatics: (wtg: 10 Marks) Axial Line ο ‘E’ due to a dipole Equitorial line ο ‘E’ due to a circular ring ο A dipole inside a uniform/non-uniform external Electric field (Torque & P.E) ο Potential due to a dipole Axial Equitorial ππ ο Potential due to a point charge ( π ) ο Potential due to a ring. ο Relation b/w ‘E’ & V, uniform field non-uniform field ο Gauss law & its proof. ο Application of Gauss law to find ‘E’ for ππ a. point charge ( ) b. Line charge ( c. Surface charge (2π ) d. π π 2ππ0 π π ) 0 Volume charge ππ (3π ) 0 ο Electric potential Energy due to a system of charges. π0 π΄ ο Capacitance of II plate capacitor ( π ππ1 π2 ( ) 1 ο Energy stored: U = 2CV2 ο Loss of P.E. when two charged capacitor are joined together. βU= πΆ1 πΆ2 (π1 −π2 )2 2(πΆ1 +πΆ2 ) Devices: Van-de – graff-Generator (2) Current Electricity: (wtg: 10 marks) (2) ο ‘Ohm’ law & its theoretical proof. ο Kirchhoff’s law and its applications. ο Net resistance in an unbalanced bridge. Wheat stone Bridge: R1 R2 R3 R2 R1 π ) R= 2π 1 π 2 +π 3 (π 1 +π 2 ) π 1 +π 2 +2π 3 Series combination of cells : I = ππΈ π +ππ ο Parallel combination of cells: I = ο Derivation of Devices: ππΈ ππ +π πΈ πΈ ( 1+ 2) π1 π2 Enet = 1 1 + π1 π2 1. Potentiometer.{to find E1/E2 & to find internal res.of a cell. 2. Meten Bridge 3. Magnetism : (Wtg: 10 Marks) ο ‘B’ due to a straight wire. B= π0 I 4π π [ Sin∅1 + Sin∅2 ] ο ‘B’ due to a circular of ring & straight current carrying wire. ο Ampere’s(Regular & irregular path) circuital law and its proof. ο Application of ampere circuital law ‘B’ due to straight wire Solenoid B= πonI Totroid ο Force on a current carrying wire and on a moving change. ο Mutual force b/w two parallel wires. ο Torque experienced by a current carrying coil palced inside a uniform external magnetic field: ; Torque = NIAB Sinπ ο ππ = 1 + π₯π ο Torque on a Bar-Magnet (Magnetic dipole) inside a uniform external field. ο P.E. of a dipole. ο Relation b/w true dip and apparent dip and apparent dip. Devices: (3) (1) Cyclotron (2) Moving coil Galvanometer and its conversion to A & V EMI, A.C ο Motional Emf in a moving rod π = -Blv. ο Motional Emf of a rotating rod π = ½ Bl2w. ο Self inductance of a long solenoid. ο Mutual inductance of two solenoid. 1 ο Magnetic energy stored in a coil U = 2 LI2 ο Eav = 2π0 ο Erms = π π0 √2 and Iav = , Irms = √2 Pure resistive Pure Inductive Pure capacitive RC Circuit LC Circuit LR Circuit LCR Circuit Variation of impendence with frequency of applied AC source. Devices: (4) π πΌ0 ο A.C Circuits ο ο ο ο 2πΌ0 Phasor diagram Average power loss in an AC circuit Pav = Irm Vrm Cos∅. Q-factor. Resonance and its applications. (1) AC Generator (2) Transformer. Ray Optics: 1 ο Mirror Formula π = 1 1 π£ + π’, m= − π’ π£ ο Refraction at spherical surface: π1 π£ π1 π£ − π2 − π’ π2 π’ = = π2 −π1 For Both convex & concave surfaces. π π1 −π2 π ο Real and apparent-depth. π‘ ο Lateral shift d= cos π sin(π − π) ο lens makes formula: & its application 1 π2 1 1 = ( − 1) ( − ) π π1 π 1 π 2 1 ο Combination of lenses ο Lens formula: 1 π 1 =π£− ο πΏπ = (π -1)A, π = sin 1 1 1 π2 (π = π + 1 π£ , m=π’ π’ (πΏπ+π΄) 2 ) π΄ /π ππ 2 , πΏ + A = I + e. ο Magnifying power of microscope. Simple: m = 1 + D/fe. compound: π£ π· m = π’0 (1 + π ) 0 π ο Magnifying power of Telescope: At LDDV: π π m = π0 (1 + π·π) π π for normal vision m = π0 π Devices: (1) Astromical & Terrestrial Telescope Reflecting (2) (3) Microscope Eyes. Simple & compound. Wave optics ο Intensity I = a2 + b2 + 2abcos∅, ∅ = 2nπ Maximum π·π ∅ = (2π − 1) 2π ο YDSE: Derivation of yn = & Minimum π·ππ Maximum n= 0,1,2,-------- π π·π yn = (2n-1)2π Minimum n= 1,2,3, ----------- ο Relation b/w intensity maxima and intensity at a general point on the screen: i.e. I = I0 Cos2∅/2 , ο SLDE: ∅ Phase diff. b/w maxima pt. & genera point on the screen. Derivation of yn-1 = (2n-1) yn = Derivation of 2π Maxima, n≠0, n≠1, n= 2,3,-------- π·ππ Minima, n≠ 0, n=1,2,3----------- π 2ππ πππ ο Resolving power of microscope: Resolving power of Telescope Rp = π·π Rp = ( 1.22π ) π· 1.22π ο Malus law I=I0cos2π ο Brewster Law: π = tan ip (6) Atomic Nucleus: ο Bohr model & Derivation of vn , rn & En of an electon revolving in nth orbit of a H & H-like atom. 1 1 1 ο Derivation of πΎ = π = Ry Z2 (π2 − π2 ) π π Ry = Rydberg constant. ο Binding Energy B.E = (βπ) c2, βπ = mass defect. for numerical case: B.E. = βπ (amu) x 931.5 Me ο Derivation of T1/2 = 1 {tav = π & (7) 0.693 , N= N0e-λt, A=A0 e-λt π π π0 = π΄ π΄0 1 π = (2) , n= π π‘ 1/2 } Dual Nature: ο λ= 12.27π΄0 π ο Davission – Germen Experiment. ο Photo- electric effect. 1243 ο Vs = π(ππ) ππ£ − π€0 (ππ£) (8) Semiconductors: ο Energy-Band Theory & difference b/w metals semiconductors and insulator on the basis of Energy-bands. ο Formation of N-types and P-type semiconductors. ο Forward & Reverse bias characteristics of Jn. diode. ο Application of Jn. diodes. οΆ Half & full wave rectifier οΆ LED & Photo diodes οΆ Solar cells οΆ Zener diodes IB ο Jn-transister: Formation & its type ο Transister action. Input ο CE-transister characterstic VBE Output. ο Transistor parameter πΌ, π½, π΄π£ ,gm & their interrelation. ο Transistor as a switch pnp an amplifier an Oscillator npn ο Logic Gates: NOT, OR, AND, NAND, NOR, X-OR symbols, Truth Tables and mathematical expressions. (9) P.O.C.: ο ο ο ο ο Modulation & its need. Circuit of AM and its demodulation. Band-width of different modes of communication & different channels. Ground-wave, sky wave & satellite communication. Optical communication (Qualitative ideas only).