Problem Types & Solved Examples

🎯 Problem-Solving Framework
Every problem here follows: Given → What Examiner Tests → Concept Selection → Solution → Shortcut Insight. This is not about memorizing solutions. This is about learning thinking patterns.

Type 1: Direct Formula Problems

Problem 1.1 CBSE Easy
In an intrinsic semiconductor, the electron concentration is 1.5 × 1010 cm-3 at room temperature. What is the hole concentration?
🧠 What Examiner Tests
Understanding of intrinsic semiconductor property: n = p = ni
Problem 1.2 NEET/JEE Main
An LED emits red light of wavelength 660 nm. Calculate the band gap energy of the semiconductor material used. (h = 6.63 × 10-34 J·s, c = 3 × 108 m/s, 1 eV = 1.6 × 10-19 J)
🧠 What Examiner Tests
Application of E = hc/λ and conversion between J and eV. Also tests quick formula: E(eV) = 1240/λ(nm)

Type 2: Conceptual Problems (No Calculation)

Problem 2.1 NEET/CBSE
A pure silicon crystal is doped with phosphorus atoms. What type of semiconductor is formed, and what are the majority charge carriers?
🧠 What Examiner Tests
Understanding of doping: pentavalent = n-type, trivalent = p-type

Type 3: Multi-Step Numerical Problems

Problem 3.1 JEE Main
A full-wave rectifier uses a transformer with secondary voltage of 20 V RMS. If the load resistance is 500 Ω and each diode has a forward resistance of 10 Ω, calculate: (a) Peak voltage (b) DC output voltage (c) DC current through load (d) Efficiency
🧠 What Examiner Tests
Multi-step problem combining: RMS to peak conversion, rectifier formulas, current calculation, efficiency

Type 4: Graph & Characteristic-Based Problems

Problem 4.1 CBSE/JEE Main
The I-V characteristic of a diode shows that at a forward voltage of 0.7 V, the current is 10 mA, and at 0.8 V, the current is 40 mA. Calculate the dynamic resistance of the diode between these two points.
🧠 What Examiner Tests
Understanding of dynamic resistance: rd = ΔV/ΔI (NOT V/I)

Type 5: Logic Gate Problems

Problem 5.1 NEET
If inputs to a NAND gate are A = 1 and B = 1, what is the output?

Type 6: Assertion-Reason (CBSE Pattern)

Problem 6.1 CBSE
Assertion (A): In forward bias, the depletion region width of a p-n junction decreases.
Reason (R): Forward bias reduces the barrier potential across the junction.

(a) Both A and R are true, and R is the correct explanation of A
(b) Both A and R are true, but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true