Full Syllabus Cheatsheet : Physics Class 12

Table of Contents
1. Chapter 1: Electric Charges and Fields
2. Chapter 2: Electrostatic Potential and Capacitance
3. Chapter 3: Current Electricity
4. Chapter 4: Moving Charges and Magnetism
5. Chapter 5: Magnetism and Matter
6. Chapter 6: Electromagnetic Induction
7. Chapter 7: Alternating Current
8. Chapter 8: Electromagnetic Waves
9. Chapter 9: Ray Optics and Optical Instruments
10. Chapter 10: Wave Optics
11. Chapter 11: Dual Nature of Radiation and Matter
12. Chapter 12: Atoms
13. Chapter 13: Nuclei
14. Chapter 14: Semiconductor Electronics
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Chapter 1: Electric Charges and Fields

Electric Charge

• Properties: Additive, conserved, quantized $q = ne$, $e = 1.6\times10^{-19}\text{ C}$
• Types: Positive and negative
• Conservation: Charge in isolated system constant
• Quantization: Charge in discrete packets

Coulomb's Law

• Scalar: $F = k\frac{q_1 q_2}{r^2}$
• Vector: $\vec{F} = k\frac{q_1 q_2}{r^2} \hat{r}$
• Superposition: Net force = vector sum

Electric Field

• Definition: $\vec{E} = \frac{\vec{F}}{q_0}$
• Point charge: $E = k\frac{q}{r^2}$
• Direction: out of $+q$, into $-q$
• Superposition: $\vec{E}_{\text{net}} = \sum \vec{E_i}$

Electric Field Lines

• Start on $+$, end on $-$
• Never intersect
• Density $\propto$ strength
• Tangent = direction

Electric Dipole

• Moment: $\vec{p} = q(2a)$
• Axial field: $E = \frac{2kp}{r^3}$
• Equatorial: $E = \frac{kp}{r^3}$
• Torque: $\vec{\tau} = \vec{p}\times\vec{E}$, $\tau=pE\sin\theta$
• Energy: $U=-\vec{p}\cdot\vec{E}= -pE\cos\theta$

Electric Flux

• $\phi = \vec{E}\cdot\vec{A} = EA\cos\theta$

Gauss's Law

• $\phi = \frac{q_{\text{enc}}}{\epsilon_0}$
• $\epsilon_0 = 8.85\times10^{-12}$

Applications

• Infinite line: $E = \frac{\lambda}{2\pi\epsilon_0 r}$
• Plane sheet: $E = \frac{\sigma}{2\epsilon_0}$
• Spherical shell: inside $E=0$, outside $E=kQ/r^2$
• Solid sphere: inside $E=\frac{kQr}{R^3}$, outside $kQ/r^2$

Chapter 2: Electrostatic Potential and Capacitance

Electrostatic Potential

• Definition: Work per unit charge from infinity
• $V = \frac{W}{q} = k\frac{q}{r}$
• Potential difference: $V_{AB}=V_A-V_B = -\int \vec{E}\cdot d\vec{l}$
• Relation: $E=-\frac{dV}{dr}$

Potential for Charge Distributions

• Point charge: $V=k\frac{q}{r}$
• Dipole axial: $V=\frac{2kp\cos\theta}{r^2}$
• Dipole equatorial: $V=0$
• Spherical shell:
  • Inside: $V=\frac{kQ}{R}$
  • Outside: $V=\frac{kQ}{r}$
• Charged ring: $V = \frac{kQ}{\sqrt{r^2 + R^2}}$

Equipotential Surfaces

• Same potential everywhere
• No work moving charge
• $\vec{E} \perp$ equipotential
• Never intersect

Potential Energy

• Two charges: $U = k\frac{q_1 q_2}{r}$
• Many charges: $U = \frac{1}{2}\sum q_i V_i$

Capacitance

• $C = \frac{Q}{V}$, unit Farad
• Parallel plates: $C = \epsilon_0\frac{A}{d}$
• With dielectric: $C = K\epsilon_0\frac{A}{d}$

Energy of Capacitor

• $U=\frac{1}{2}QV=\frac{1}{2}CV^2=\frac{Q^2}{2C}$
• Energy density: $u=\frac{1}{2}\epsilon_0E^2$

Combination of Capacitors

• Series: $\frac{1}{C_{\text{eq}}}=\frac{1}{C_1}+\frac{1}{C_2}+...$
• Parallel: $C_{\text{eq}}=C_1+C_2+...$

Common Forms

• Spherical: $C=4\pi\epsilon_0R$
• Cylindrical: $C= \frac{2\pi\epsilon_0\ell}{\ln(b/a)}$

Van de Graaff Generator

• Produces very high voltage
• Belt transfers charge to sphere
• Order of MV

Chapter 3: Current Electricity

Electric Current

• $I = \frac{Q}{t}$, unit Ampere
• Conventional direction $+ \to -$
• Drift velocity: $v_d=\frac{I}{nAe}$

Ohm's Law

• $V = IR$
• Fails at high T, semiconductors etc.

Resistance & Resistivity

• $R=\rho\frac{l}{A}$
• Conductivity: $\sigma=\frac{1}{\rho}$
• Temperature: $\rho_T=\rho_0(1+\alpha\Delta T)$

Series & Parallel

• Series: $R_{\text{eq}}=R_1+R_2+...$
• Parallel: $\frac{1}{R_{\text{eq}}} = \frac{1}{R_1}+\frac{1}{R_2}+...$

Kirchhoff Laws

• KCL: $\Sigma I_{\text{in}}=\Sigma I_{\text{out}}$
• KVL: $\Sigma V=0$

Power & Energy

• $P=VI=I^2R=\frac{V^2}{R}$
• $E=Pt=VIt$

EMF & Internal Resistance

• $V=\varepsilon - Ir$
• Series cells: $\varepsilon_{\text{eq}}=n\varepsilon, r_{\text{eq}}=nr$
• Parallel: $\varepsilon_{\text{eq}}=\varepsilon, r_{\text{eq}}=\frac{r}{n}$

Wheatstone Bridge

• Balance condition: $\frac{P}{Q}=\frac{R}{S}$

Meter Bridge

• $\frac{X}{R}=\frac{l_1}{l_2}$, $l_1+l_2=100\,\text{cm}$

Potentiometer

• Principle $V\propto l$
• No current drawn at null point

Heating Effect

• Joule heat: $H=I^2Rt=VIt$

Chapter 4: Moving Charges and Magnetism

Lorentz Force

• $\vec{F}=q(\vec{v}\times\vec{B})$
• Magnitude: $F=qvB\sin\theta$
• Max at $90^\circ$, zero if parallel

Motion in Magnetic Field

• Circular radius: $r=\frac{mv}{qB}$
• Time period: $T=\frac{2\pi m}{qB}$
• Frequency: $f=\frac{qB}{2\pi m}$
• Pitch (helical): $p=v_{\parallel}T$

Force on Current

• $\vec{F}=I(\vec{\ell}\times\vec{B})$
• $F=BIL\sin\theta$

Force Between Parallel Currents

• $\frac{F}{\ell}=\frac{\mu_0 I_1 I_2}{2\pi d}$
• Same direction: attract
• Opposite: repel

Torque on Loop

• $\vec{\tau}=\vec{M}\times\vec{B}$
• $\tau=NIAB\sin\theta$
• Magnetic moment: $M=NIA$

Moving Coil Galvanometer

• Current sensitivity: $I_s=\frac{\theta}{I}=\frac{NAB}{k}$
• Voltage sensitivity: $V_s=\frac{\theta}{V}=\frac{NAB}{kR}$
• Ammeter: shunt resistance
• Voltmeter: series resistance

Biot-Savart Law

• $d\vec{B}=\frac{\mu_0}{4\pi}\frac{I(d\vec{\ell}\times\vec{r})}{r^3}$
• $\mu_0=4\pi\times10^{-7}\,\text{Tm}\,\text{A}^{-1}$

Applications

• Infinite wire: $B=\frac{\mu_0 I}{2\pi d}$
• Circular loop (center): $B=\frac{\mu_0 I}{2R}$
• Loop axis: $B=\frac{\mu_0 IR^2}{2(R^2+x^2)^{3/2}}$

Ampere's Circuital Law

• $\oint \vec{B}\cdot d\vec{\ell}=\mu_0 I_{\text{enc}}$

Applications

• Solenoid: $B=\mu_0 nI$
• Toroid: $B=\frac{\mu_0 NI}{2\pi r}$

Chapter 5: Magnetism and Matter

Bar Magnet

• Moment: $M=m(2l)$
• Axial field: $B=\frac{\mu_0}{4\pi}\frac{2M}{r^3}$
• Equatorial: $B=\frac{\mu_0}{4\pi}\frac{M}{r^3}$

Torque & Energy

• $\vec{\tau}=\vec{M}\times\vec{B}$
• $\tau=MB\sin\theta$
• $U=-\vec{M}\cdot\vec{B}=-MB\cos\theta$

Earth's Magnetism

• Declination $\theta$
• DIP $\delta$
• Horizontal: $B_H=B\cos\delta$
• Vertical: $B_V=B\sin\delta$
• $B^2=B_H^2+B_V^2,\; \tan\delta=\frac{B_V}{B_H}$

Magnetic Materials

Diamagnetic

• $\chi<0$, feeble repulsion
• Cu, Bi, Au, water

Paramagnetic

• $\chi>0$, weak attraction
• Al, O₂, Pt
• Curie law: $\chi\propto\frac{1}{T}$

Ferromagnetic

• Strongly attracted
• Fe, Ni, Co
• Domains, hysteresis
• Curie temperature: loses ferromagnetism above it

Magnetic Quantities

• Magnetization: $M=\frac{\text{magnetic moment}}{\text{volume}}$
• Susceptibility: $\chi=\frac{M}{H}=\mu_r-1$
• Intensity: $H=\frac{B}{\mu_0}-M$
• Permeability: $\mu=\frac{B}{H}$
• Relative permeability: $\mu_r=\frac{\mu}{\mu_0}$

Chapter 6: Electromagnetic Induction

Magnetic Flux

• $\phi = \vec{B}\cdot\vec{A} = BA\cos\theta$
• Unit: Weber (Wb)

Faraday's Law

• $\varepsilon = -\frac{d\phi}{dt}$
• N turns: $\varepsilon = -N\frac{d\phi}{dt}$

Lenz's Law

• Induced current opposes change
• Energy conservation result

Motional EMF

• Rod in field: $\varepsilon = Blv$
• Rotating rod: $\varepsilon = \frac{1}{2} B\omega l^2$

Eddy Currents

• Loop currents induced in bulk conductors
• Applications: brakes, furnaces, meters
• Reduced by lamination

Self Inductance

• $\varepsilon = -L\frac{dI}{dt}$
• Solenoid: $L=\mu_0 n^2 A l = \mu_0\frac{N^2A}{l}$
• Energy stored: $U=\frac{1}{2} LI^2$

Mutual Inductance

• $\varepsilon_2 = -M\frac{dI_1}{dt}$
• Two solenoids: $M=\mu_0 n_1 n_2 A l$
• $M_{12}=M_{21}$

AC Generator

• Principle: electromagnetic induction
• $\varepsilon = \varepsilon_0 \sin\omega t = NAB\omega \sin\omega t$
• Converts mechanical to electrical energy

Chapter 7: Alternating Current

AC Basics

• Voltage: $V=V_0\sin\omega t$
• Current: $I=I_0\sin(\omega t\pm\phi)$
• RMS: $V_{\text{rms}}=\frac{V_0}{\sqrt{2}},\; I_{\text{rms}}=\frac{I_0}{\sqrt{2}}$
• Average power: $P_{\text{avg}}=V_{\text{rms}} I_{\text{rms}} \cos\phi$

Resistor (R)

• V and I in phase
• $V=IR$
• Power: $P=I^2R$

Inductor (L)

• I lags V by $90^\circ$
• Reactance: $X_L=\omega L=2\pi f L$
• $V=IX_L$
• No power absorbed

Capacitor (C)

• I leads V by $90^\circ$
• Reactance: $X_C=\frac{1}{\omega C}=\frac{1}{2\pi f C}$
• $V=IX_C$
• No power absorbed

Series LCR Circuit

• Impedance: $Z=\sqrt{R^2+(X_L-X_C)^2}$
• Current: $I=\frac{V}{Z}$
• Phase: $\tan\phi=\frac{X_L-X_C}{R}$
• Power factor: $\cos\phi=\frac{R}{Z}$
• Resonance: $X_L=X_C$, $\omega_0=\frac{1}{\sqrt{LC}}$
• At resonance: $Z=R$, current max

Power in AC

• Instantaneous: $P=VI$
• Average: $P=V_{\text{rms}} I_{\text{rms}}\cos\phi$
• Wattless current: $I\sin\phi$

LC Oscillations

• Frequency: $f=\frac{1}{2\pi\sqrt{LC}}$
• Energy alternates between fields

Transformer

• Principle: mutual induction
• Turns ratio: $\frac{N_s}{N_p}=\frac{V_s}{V_p}=\frac{I_p}{I_s}$
• Efficiency: $\eta=\frac{\text{output}}{\text{input}}\times100\%$
• Step-up: $N_s>N_p$, Step-down: $N_s
• Losses: copper, eddy, hysteresis, flux leakage

Chapter 8: Electromagnetic Waves

Displacement Current

• $I_d = \epsilon_0 \frac{d\phi_E}{dt}$
• Adds to conduction current in Ampere's law
• Explains magnetic field in capacitor

Maxwell's Equations

1. Gauss (E): $\oint \vec{E}\cdot d\vec{A}= \frac{q}{\epsilon_0}$
2. Gauss (B): $\oint \vec{B}\cdot d\vec{A}= 0$
3. Faraday: $\oint \vec{E}\cdot d\vec{\ell}= -\frac{d\phi_B}{dt}$
4. Ampere-Maxwell: $\oint \vec{B}\cdot d\vec{\ell}= \mu_0(I + I_d)$

Electromagnetic Waves

• Oscillating electric and magnetic fields
• $\vec{E}\perp \vec{B}\perp \text{propagation}$
• Speed: $c=\frac{1}{\sqrt{\mu_0\epsilon_0}}=3\times10^8 \text{ m/s}$
• Relation: $c=f\lambda$
• Energy equally shared in E and B

Wave Properties

• No medium required
• Transport energy & momentum
• Show interference, diffraction, polarization
• Intensity: $I=\frac{1}{2} \epsilon_0 E_0^2 c=\frac{c}{2\mu_0}B_0^2$

Electromagnetic Spectrum

1. Radio: $\lambda>0.1\,\text{m}$
2. Microwave: $1\,\text{mm}-0.1\,\text{m}$
3. Infrared: $700\,\text{nm}-1\,\text{mm}$
4. Visible: $400-700\,\text{nm}$
5. Ultraviolet: $10-400\,\text{nm}$
6. X-rays: $0.01-10\,\text{nm}$
7. Gamma: $\lambda<0.01\,\text{nm}$

Key Ideas

• Energy $\propto \nu$
• $\lambda=\frac{c}{\nu}$
• Higher frequency ⇒ more penetrating

Chapter 9: Ray Optics and Optical Instruments

Reflection of Light

• Incident ray, reflected ray, normal same plane
• $i=r$

Spherical Mirrors

• Mirror formula: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
• Magnification: $m=-\frac{v}{u}=\frac{h'}{h}$
• Focal length: $f=\frac{R}{2}$
• Concave: $f<0$, real/virtual
• Convex: $f>0$, virtual only

Refraction

• Snell's law: $n_1\sin\theta_1=n_2\sin\theta_2$
• RI: $n=\frac{c}{v} = \frac{\lambda_0}{\lambda_m}$
• Relative RI: $n_{21}=\frac{n_2}{n_1}$

Total Internal Reflection

• Dense to rare medium only
• Critical angle: $\sin C = \frac{n_2}{n_1}= \frac{1}{n}$ (air)
• Applications: fiber, mirage, diamond

Spherical Refraction

• $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$
• Plane surface: $v=-\frac{n_2}{n_1}u$

Thin Lens Formula

• $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
• Magnification: $m=\frac{v}{u}=\frac{h'}{h}$
• Lens maker: $\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
• Power $P=\frac{1}{f}$ (m), in Dioptre
• Convex: $f>0$, Concave: $f<0$

Lens Combination

• Contact: $P=P_1+P_2$, $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
• Separated $d$: $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2}$

Prism

• Deviation: $\delta=i+e-A$
• Minimum deviation: $\delta_m$, $i=e=\frac{A+\delta_m}{2}$
• RI: $n=\frac{\sin((A+\delta_m)/2)}{\sin(A/2)}$

Dispersion

• Splitting of white light
• Angular: $\theta=(n_v-n_r)A$
• Dispersive power: $\omega=\frac{n_v-n_r}{n_y-1}$

Optical Instruments

Simple Microscope

• At infinity: $m=\frac{D}{f}$
• At D: $m=1+\frac{D}{f}$

Compound Microscope

• Total: $m=m_o m_e=\left(\frac{v_o}{u_o}\right)\left(\frac{D}{f_e}\right)$
• Normal adjustment: $m=-\frac{L}{f_o}\frac{D}{f_e}$

Telescope

• Magnification: $m=\frac{f_o}{f_e}$
• Normal adjustment: $L=f_o+f_e$

Chapter 10: Wave Optics

Huygens' Principle

Every point on a wavefront acts as a secondary source

New wavefront = envelope of secondary wavelets

Explains reflection, refraction, diffraction

Interference

Superposition of coherent waves

Constructive: path $\Delta = n\lambda$, phase $= 2n\pi$

Destructive: $\Delta = \frac{(2n-1)\lambda}{2}$, phase $= (2n-1)\pi$

Young's Double Slit Experiment

Fringe width: $\beta = \frac{\lambda D}{d}$

Bright: $y_n = n\frac{\lambda D}{d}$

Dark: $y_n = (2n-1)\frac{\lambda D}{2d}$

Intensity: $I = 4I_0\cos^2(\phi/2)$, $\phi = \frac{2\pi d}{\lambda D}y$

Conditions for Interference

Coherent sources

Same frequency and wavelength

Prefer similar amplitude

Close spacing

Diffraction

Bending of waves around obstacles

Single slit minima: $a\sin\theta = n\lambda$

Central maximum width: $2\frac{\lambda D}{a}$

Fresnel (near-field) & Fraunhofer (far-field)

Polarization

Light vibration confined to one plane

Malus law: $I = I_0\cos^2\theta$

Brewster angle: $\tan\theta_p = \frac{n_2}{n_1}$

Methods: reflection, refraction, scattering, polaroids

Resolving Power

Telescope: $R = \frac{a}{1.22\lambda}$

Microscope: $R = \frac{2n\sin\theta}{1.22\lambda}$

Smaller $\lambda \rightarrow$ better resolution

Chapter 11: Dual Nature of Radiation and Matter

Photoelectric Effect

Electron emission by light

Observations:

1. Instantaneous emission

2. Threshold frequency $\nu_0$

3. KE depends on frequency, not intensity

4. Current $\propto$ intensity

Einstein Equation

$h\nu = \phi + KE_{\max}$

$\phi = h\nu_0$

$KE_{\max} = eV_0$

Full: $h\nu = h\nu_0 + \frac{1}{2}mv_{\max}^2 = h\nu_0 + eV_0$

Photon

Energy: $E = h\nu = \frac{hc}{\lambda}$

Momentum: $p = \frac{E}{c} = \frac{h}{\lambda}$

Planck constant $h = 6.63 \times 10^{-34}$ Js

Matter Waves (de Broglie)

$\lambda = \frac{h}{p} = \frac{h}{mv}$

Accelerated charge: $\lambda = \frac{h}{\sqrt{2mqV}}$

Davisson-Germer Experiment

Electron diffraction confirms wave nature

$\lambda = \frac{h}{\sqrt{2m_eV}}$

Useful Relations

$E(\text{eV}) = \frac{12400}{\lambda(\text{Å})}$

$\lambda(\text{Å}) = \frac{12.27}{\sqrt{V}}$ (electrons)

Chapter 12: Atoms

Thomson Model

• Electrons embedded in positively charged sphere
• Could not explain spectra & stability

Rutherford Model

• Alpha scattering experiment
• Most mass concentrated in nucleus
• Electrons orbit nucleus
• Failed to explain stability & line spectra

Bohr Model

Postulates

• Electrons revolve in stable orbits
• Angular momentum: $mvr=\frac{nh}{2\pi}$
• Energy absorbed/emitted: $h\nu=E_i-E_f$

Hydrogen Atom Results

• Radius: $r_n=\frac{n^2 h^2 \epsilon_0}{\pi m e^2}=0.529n^2 \text{ Å}$
• Velocity: $v_n \propto \frac{1}{n}$
• Energy: $E_n=-\frac{13.6}{n^2} \text{ eV}$
• Frequency: $\nu=R c\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

Hydrogen Spectrum

• Lyman: $n_1=1$ (UV)
• Balmer: $n_1=2$ (visible)
• Paschen: $n_1=3$ (IR)
• Brackett: $n_1=4$ (IR)
• Pfund: $n_1=5$ (IR)

Rydberg Formula

• $\frac{1}{\lambda}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$
• R = $1.097\times10^7 \text{ m}^{-1}$

Limitations

• Only single-electron atoms
• No fine structure or spectra details
• Incompatible with uncertainty principle

Chapter 13: Nuclei

Nuclear Structure

• Notation: ${}^A_Z X$
• Mass number: $A=Z+N$
• Radius: $R=R_0 A^{1/3}$, $R_0=1.2\,\text{fm}$
• Nuclear density ≈ constant: $2.3\times10^{17} \text{ kg/m}^3$

Atomic Mass Unit

• 1 u = $\frac{1}{12}$ mass of C-12 atom
• 1 u = $1.66\times10^{-27} \text{ kg}$
• Equivalent: $931.5 \text{ MeV}/c^2$

Mass Defect & Binding Energy

• $\Delta m = [Zm_p + N m_n - M_{\text{nucleus}}]$
• $BE=\Delta m c^2 = \Delta m \times 931.5 \text{ MeV}$
• $BE/A$ max ~ 8.8 MeV (Fe-56)

Nuclear Force

• Short range (~ $10^{-15}$ m)
• Very strong & charge-independent
• Saturates (each nucleon interacts with few neighbours)

Radioactivity

• Spontaneous decay

Types

• $\alpha$: ${}^A_Z X \rightarrow {}^{A-4}_{Z-2}Y + {}^4_2He$
• $\beta^-$: ${}^A_Z X \rightarrow {}^{A}_{Z+1}Y + e^- + \bar{\nu}$
• $\beta^+$: ${}^A_Z X \rightarrow {}^{A}_{Z-1}Y + e^+ + \nu$
• $\gamma$: Nucleus → same nucleus + $\gamma$

Decay Law

• $A = -\frac{dN}{dt} = \lambda N$
• $N=N_0 e^{-\lambda t}$
• Half-life: $T_{1/2}=\frac{0.693}{\lambda}$
• Mean life: $\tau=\frac{1}{\lambda}=\frac{T_{1/2}}{0.693}$
• Activity: $A=A_0 e^{-\lambda t}$

Nuclear Reactions

• Q-value: $Q=(m_{\text{reactants}}-m_{\text{products}})c^2$
• Q>0 exothermic, Q<0 endothermic

Fission

• Splitting of heavy nucleus
• ${}^{235}U + n \rightarrow {}^{141}Ba + {}^{92}Kr + 3n + \text{energy}$
• Chain reaction
• Used in reactors & bombs

Fusion

• Light nuclei combine
• ${}^2H + {}^3H \rightarrow {}^4He + n + 17.6\,\text{MeV}$
• Requires very high temperature (~ $10^7$ K)
• Energy in stars

Chapter 14: Semiconductor Electronics

Intrinsic Semiconductors

• Pure Si or Ge (group IV)
• At 0 K → insulator
• At room T → electrons + holes
• $n_e=n_h$
• Energy gap: Si ≈ 1.1 eV, Ge ≈ 0.7 eV

Extrinsic Semiconductors

n-type

• Doped with group V (P, As)
• Electrons majority, holes minority

p-type

• Doped with group III (B, Ga)
• Holes majority, electrons minority

PN Junction

• Depletion region
• Barrier potential ~ 0.7 V (Si)
• Forward bias → current flows
• Reverse bias → negligible current

Characteristics

• Forward I rises exponentially
• Reverse current small until breakdown

Diode Applications

• Rectification (half-wave, full-wave)
• Clipping & clamping
• Voltage regulator (Zener)

Transistors (BJT)

• Types: n-p-n, p-n-p
• Regions: emitter, base, collector
• Amplification: $\beta = \frac{I_c}{I_b}$
• Modes: cutoff, active, saturation

Logic Gates

• Basic: AND, OR, NOT
• Derived: NAND, NOR (universal)
• Boolean algebra