Ohm's law — microscopic origin, resistivity: Foundations

1.8.16 · D1 · Physics › Electromagnetism › Ohm's law — microscopic origin, resistivity

Is page par koi bhi assumption nahi hai. Ohm's law — microscopic origin, resistivity padhne se pehle, tumhe har woh letter fluently samajhna chahiye jo woh likhta hai. Neeche, har symbol ko teen cheezein milti hain: ek plain-words meaning, ek picture, aur topic ko woh kyun chahiye. Inhe is tarah order kiya gaya hai ki har ek sirf pehle se bani ideas use kare.

0. Scene: wire ke andar kya hota hai?

Ek copper wire ko ek billion baar zoom in karke socho. Tum ek saaf grid dekhoge heavy atoms ka jo apni jagah pe lock hain — lattice — aur ek swarm of light, loose electrons jo freely unke beech wander karte hain, jaise ek godown ki shelves mein flies.

Do facts yaad rakhne ke liye:

Atoms fixed hain (woh sirf apni jagah jiggle karte hain — garam hone par zyada jiggle).
Electrons roam karne ke liye free hain — ye hi woh cheezein hain jo actually wire ke andar move karti hain aur current banati hain.

1. Charge, aur electron ka charge $e$

Plain words: Charge woh property hai jo particles ko electric pushes aur pulls feel karati hai. Hum ise coulombs (C) mein measure karte hain.

Picture: ise ek particle par ek invisible "tag" ki tarah socho jo kehta hai yeh cheez electric world mein kitni strongly grab hoti hai.

Topic ko kyun chahiye: electrons par har force aur current ka har bit $e$ ke multiples mein count hota hai. Iske bina hum "kitne electrons move hue" ko "kitna current" mein convert nahi kar sakte.

2. Electric field $E$ — push, arrows ke roop mein

Plain words: kisi point par electric field tumhe batata hai ki ek unit positive charge wahan kitna force feel karega. Iska ek size aur direction hota hai, isliye hum ise ek arrow ke roop mein draw karte hain aur upar ek tiny arrow ke saath likhte hain: $E$ .

Picture: imagine karo wire mein har point par ek arrow, sab ek hi taraf point karte hue (wire ke neeche). Ek positive charge arrow ke saath push hota hai; negative electron opposite push hota hai.

Topic ko kyun chahiye: $E$ push hai. Dekho Electric field inside a conductor — yeh samajhne ke liye ki wire ke andar steady $E$ exist kyun kar sakti hai.

3. Voltage $V$ — push, total ke roop mein count ki gayi

Plain words: voltage (ya potential difference) wire ke dono ends ke beech total "electric shove" hai. Agar field push per metre hai, toh voltage poori length par add up ki gayi push hai.

Picture: ek hill. Field har jagah steepness hai; voltage total drop hai upar se neeche tak. Ek ball steepness ki wajah se neeche girti hai; woh jitni total distance gir sakti hai woh voltage hai.

Topic ko kyun chahiye: macroscopic law hai $V = I R$ . Ise electrons jo feel karte hain ( $E$ ) se connect karne ke liye, hume yeh bridge $E = V / L$ chahiye.

4. Speed, velocity $v$ , aur acceleration $a$

Plain words:

Speed = kitna fast (ek plain number).
Velocity $v$ = kitna fast aur kis direction mein (ek arrow).
Acceleration $a$ = velocity kitni fast change ho rahi hai (yeh bhi ek arrow).

Picture: wire ke saath ek dot move ho rahi hai. Uski velocity ek arrow hai jo abhi uski motion show karta hai; agar woh arrow grow ho raha hai, toh woh accelerate ho raha hai.

Topic ko kyun chahiye: poori derivation ka step 1 hai force → acceleration via $a = F / m$ . Yeh honest starting point hai "ek electron kya karta hai" ke liye.

5. Drift velocity $v_{d}$ — slow crawl, fast wiggle nahi

Yeh subtle wala hai. Electrons pehle se hi heat ki wajah se fast aur randomly ud rahe hain — lekin woh random motion har taraf jaati hai aur cancel out ho jaati hai: wire ke andar koi net travel nahi.

Picture (figure above): left panel ek electron ka real path dikhata hai — ek jagged random walk jo thoda downstream lean karta hai. Right panel wiggle hata kar sirf lean dikhata hai: woh lean hi $v_{d}$ hai.

Topic ko kyun chahiye: current net charge flow hai. Sirf drift $v_{d}$ net hai, isliye woh har current formula ka star hai.

6. Relaxation time $τ$ — bumps ke beech average gap

Plain words: $τ$ (Greek letter "tau") wo average time hai jab ek electron lattice ke saath do collisions ke beech freely fly karta hai.

Picture: random-walk figure mein, $τ$ ek straight segment ki average length (time mein) hai agle kink se pehle.

Topic ko kyun chahiye: $τ$ hi hai jo "hamesha ke liye accelerate karta hai" ko "steady drift tak pahunchta hai" mein badalta hai. Yeh Drude model of conduction ke center mein aur $σ = n e^{2} τ / m$ ke andar baitha hai.

7. Number density $n$ — electrons kitne crowded hain

Plain words: $n$ metal ke har cubic metre mein pack hue free electrons ki number hai.

Picture: ek $1 m \times 1 m \times 1 m$ box ke andar roaming dots gino. Copper ke liye woh count ek staggering $n \approx 8.5 \times 1 0^{28}$ per m³ hai.

Topic ko kyun chahiye: zyada carriers → har second zyada charge sweep hoga → zyada current. $n$ dono $J = n e v_{d}$ aur $σ = n e^{2} τ / m$ mein aata hai.

8. Cross-sectional area $A$ aur length $L$ — wire ki shape

Plain words:

$A$ = wire ke circular face ka area (m²) — woh kitni moti hai.
$L$ = wire ki length (m) — woh kitni lambi hai.

Picture: wire ko seedha cross karke kaato; jo flat disc tum expose karte ho uska area $A$ hai. Ise end to end stretch karo; woh distance $L$ hai.

Topic ko kyun chahiye: geometry ( $L$ , $A$ ) hi material property $ρ$ ko real resistance $R = ρ L / A$ mein badalta hai. Dekho Resistors in series and parallel.

9. Current $I$ aur current density $J$

Plain words:

Current $I$ = charge per second ek point se guzarta hai (units: amperes, A = C/s).
Current density $J$ = current per unit area (A/m²), ek arrow jo charge flow ki direction dikhata hai.

Picture: $I$ total river flow hai; $J$ hai ki paani riverbed mein har jagah kitna hard rush karta hai.

Topic ko kyun chahiye: yeh microscopic drift ko measurable current mein convert karte hain. Deep dive: Electric current and current density.

10. Conductivity $σ$ , resistivity $ρ$ , resistance $R$

Ab payoff symbols — sab bas "current kitni easily flow karta hai" ke names hain.

Picture: $ρ$ material ki "muddiness" hai; $R$ is specific muddy field ko cross karne ki total struggle hai, jo is par bhi depend karta hai ki path kitna lamba aur narrow hai.

Topic ko kyun chahiye: $σ$ , $ρ$ , $R$ destination hain. Poori derivation inhe $n, e, τ, m$ se compute karne ke liye hai.

Map: yeh topic ko kaise feed karte hain

Equipment checklist

Khud test karo — right side cover karo aur zor se jawab do.

E

mein arrow-hat ka kya matlab hai?

Quantity ek vector hai — iska direction hai, arrow ke roop mein draw hota hai, sirf number nahi.

Ek electron par charge kya hai, symbol aur value?

- e

, jahan

e = 1.6 \times 1 0^{- 19} C

Field

E

mein electron par force?

F = - e E

(field ke along backward).

Force aur motion ko jodata Newton's second law?

a = F / m

Random thermal motion aur drift velocity mein antar?

Thermal motion fast aur random hai, zero average ho jaati hai (koi net current nahi); drift

v_{d}

tiny net crawl hai

E

ke along.

τ

(relaxation time) kya hai?

Average time jab ek electron collisions ke beech freely fly karta hai; har bump ke baad uska drift zero reset ho jaata hai.

n

kya count karta hai?

Free electrons per cubic metre (copper ≈

8.5 \times 1 0^{28} m^{- 3}

Uniform wire mein voltage aur field relate karo?

E = V / L

n, e, A, v_{d}

ke terms mein current?

I = n e A v_{d}

ρ

aur

R

mein antar?

ρ

ek material property hai (koi bhi shape);

R = ρ L / A

wire ki length aur area par bhi depend karta hai.

Kaun si quantity woh "brake" hai jo runaway acceleration rokti hai?

Collisions, relaxation time

τ

mein captured.

Connections

Parent topic (Hinglish)
Electric current and current density
Electric field inside a conductor
Drude model of conduction
Drift and diffusion of carriers
Resistors in series and parallel
Temperature dependence of resistance