Chapter 22 · Class 11-12 & JEE/NEET
Semiconductors & Electronics
29 topics in 8 parts
Semiconductor conductivity Semiconductor resistivity Drift current density Carrier mobility Mass-action law Intrinsic carrier concentration
Key ideas
4. Systematic Comparison & Parameter Classifications
| Body Shape | Axis of Rotation | Moment of Inertia (I) | Shape Factor (k² / R²) |
|---|---|---|---|
| Thin Ring / Hollow Cylinder | Central Axis Perpendicular to Plane | M R² | 1.0 (Slowest Down Incline) |
| Solid Disc / Solid Cylinder | Central Axis Perpendicular to Plane | (1/2) M R² | 0.50 |
| Solid Sphere | Diameter Axis | (2/5) M R² | 0.40 (Fastest Down Incline) |
| Spherical Shell (Hollow) | Diameter Axis | (2/3) M R² | 0.67 |
| Uniform Rod (Length L) | Through Center Perpendicular to Length | (1/12) M L² | L² / (12 R²) |
Exam Worked Example
Problem: A solid sphere and a solid cylinder of equal mass M and radius R roll down the same inclined plane without slipping from rest. Find the ratio of their accelerations down the incline.
● Step 1: Formula for linear acceleration in pure rolling: a = (g sin θ) / (1 + k²/R²).
● Step 2: For solid sphere, k²/R² = 2/5 = 0.4. Therefore, a_sphere = (g sin θ) / (1 + 2/5) = 5/7 g sin θ ≈ 0.714 g sin θ.
● Step 3: For solid cylinder, k²/R² = 1/2 = 0.5. Therefore, a_cyl = (g sin θ) / (1 + 1/2) = 2/3 g sin θ ≈ 0.667 g sin θ.
● Step 4: Ratio a_sphere / a_cyl = (5/7) / (2/3) = (5 * 3) / (7 * 2) = 15 / 14 ≈ 1.07. The solid sphere reaches the bottom first!
Checkpoint
1. When a ballet dancer pulls her arms inward during a spin on smooth ice, what happens to her kinetic energy?
All 29 topics in Semiconductors & Electronics
Semiconductors
- Classification of Solids (Metals, Semiconductors & Insulators)
- Intrinsic & Extrinsic Semiconductors
- Doping (n-type & p-type)
- Electrical Conductivity & Resistivity
- Carrier Concentration & Mobility
- Energy Band Gap & Band Theory
Semiconductor Diode
- Depletion Region & Barrier Potential
- Forward & Reverse Biasing
- I-V Characteristics in Forward & Reverse Bias
- Diode Breakdown (Zener & Avalanche Breakdown)
- Diode Circuit Analysis & Resistance
Diodes as a Rectifier
- Half-Wave & Full-Wave Rectifiers
- Rectifier Efficiency & Ripple Factor
- Filter Circuits (Capacitor Filter)
I-V Characteristics
- LED
- Photodiode
- Solar Cell & Diode
Zener Diode as a Voltage Regulator
- Zener Diode Breakdown & I-V Characteristics
- Zener Diode Voltage Regulation & Circuit Analysis
Junction Transistor
- Transistor Action
- Characteristics of a Transistor
- Transistor Configurations (CB, CE, CC)
- Current Gains (Alpha & Beta)
Transistor as an Amplifier
- Common Emitter Configuration & Oscillator
- Voltage Gain, Current Gain & Power Gain
- Transistor as a Switch
Logic Gates
- Fundamental Logic Gates (OR, AND, NOT)
- Universal & Combination Logic Gates (NAND, NOR, XOR)
- Truth Tables & Boolean Expressions