Identify factors affecting resistance
Scenario
Ek lambi patli tunnel se nikalna, ek choti aur chaudi tunnel ki tulna mein zyada mushkil hota hai.
Kya wire ke andar current ke saath bhi yahi hota hai?
Mental model
Resistance, wire ki lambai aur motai (thickness) par depend karta hai.
Jitni lambi wire hogi, utni zyada rukawat aayegi (length ke proportional). Jitni moti wire hogi, utni aasani se current pass hoga (area ke inversely proportional).
Explanation
Ek metallic wire ki resistance chaar main factors par nirbhar karti hai: Length, Area of cross-section, Nature of material, aur Temperature.
Sabse pehla factor hai length (L). Resistance directly proportional hoti hai wire ki lambai ke (R ∝ L). Agar wire ko double lamba kiya jaye, toh uski resistance bhi double ho jayegi.
Doosra factor hai Area of cross-section (A). Resistance motai (thickness) ke inversely proportional hoti hai (R ∝ 1/A). Ek moti wire mein electrons ke flow ke liye zyada jagah hoti hai, toh uski resistance kam hoti hai.
Teesra hai nature of material. Copper ek accha conductor hai jabki nichrome (ek alloy) ki resistance bahut zyada hoti hai.
Chautha factor temperature hai. Metals ka temperature badhane par resistance generally badh jati hai, kyunki atoms ka vibration electrons ko obstruct karta hai.
Worked example
Problem: What are the factors on which the resistance of a conductor depends?
- Factors ko point-wise likhna hota hai.
- Baaki do important factors bhi mention karne chahiye.
Answer: Length, area of cross-section, nature of its material, and temperature.
Problem: Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source?
- Resistance aur Area ka relation yaad karte hain.
- Thick wire ka area zyada hota hai, isliye resistance kam hogi.
- Kam resistance matlab zyada current.
Answer: Thick wire, because resistance is inversely proportional to the area of cross-section.
Key points
- Length Effect: R is directly proportional to length L (R ∝ L).
- Area Effect: R is inversely proportional to cross-sectional area A (R ∝ 1/A).
Common mistakes
- Confusing length and area dependencies: Log sochte hain ki mota wire zyada resistance dega. Asal mein mota wire (zyada area) electron ko asaan path deta hai, isliye resistance kam ho jati hai.
Recall questions
- If the length of a wire is halved, what happens to its resistance?
- If the area of cross-section is doubled, what happens to the resistance?
- How does resistance depend on the length of a wire?
Questions & answers
On what factors does the resistance of a conductor depend?
Its length, area of cross-section, nature of material, and temperature.
Approach: List all four macroscopic and microscopic factors.
If a wire is stretched to double its length without changing its volume, what happens to its resistance?
It becomes four times the original resistance.
Approach: Length doubles, area halves, so R = ρ(2L)/(A/2) = 4ρL/A.
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