Define current (flow of charge) and the ampere

1.1.4 · Hardware › Electricity & Charge Basics

Current KYA hai?

Ise is tarah define KYUN karte hain? (First principles se derivation)

Hum ek aisa number chahte hain jo "flow kitna strong hai" capture kare. Do cheezein clearly matter karti hain:

Kitna charge move hua — zyada charge = stronger flow.
Kitna time laga — usi charge ko zyada time mein cover karna ek weaker flow hai.

Toh natural quantity hai charge divided by time. Shuru karte hain us total charge se jo ek surface cross karta hai:

$Q = \int I d t$

Agar current steady hai (constant), toh integral collapse ho jaata hai:

$Q = I \cdot t ⟹ I = \frac{Q}{t}$

Yeh step kyun? Integral mein se ek constant ko bahar nikaalte hain toh woh sirf time ki length se multiply hota hai. Yahi everyday form hai jo tum use karte ho.

Changing current ke liye hum limit lete hain, jo instantaneous definition deta hai:

$I = lim_{Δ t \to 0} \frac{Δ Q}{Δ t} = \frac{d Q}{d t}$

Yeh step kyun? Ek choti si window par average $Δ Q /Δ t$ wahi exact slope ban jaata hai charge-vs-time curve ka — derivative ka matlab yahi hota hai.

Charge actually KAISE move karta hai? (Microscopic picture)

Wire ke andar, current drifting electrons se carry hoti hai. Maano $n$ charge carriers hain per cubic metre, har ek charge $q$ carry karta hai, average speed $v_{d}$ se drift karta hai, ek wire mein jiska cross-sectional area $A$ hai.

Time $Δ t$ mein, carriers $v_{d} Δ t$ distance move karte hain. $A v_{d} Δ t$ volume ke cylinder ke andar saare carriers point se guzar jaate hain:

$Δ Q = q \cdot n \cdot (A v_{d} Δ t)$

Yeh step kyun? Carriers ki sankhya = density × volume; total charge = woh count × charge-each.

$Δ t$ se divide karo:

$I = n q A v_{d}$

Yeh dikhata hai ki current depend karta hai kitne carriers hain, kitna har ek carry karta hai, wire kitni wide hai, aur kitni tezi se drift karte hain.

Figure — Define current (flow of charge) and the ampere

Direction: conventional vs electron flow

Worked examples

Common mistakes

Recall Feynman: ek 12-saal ke bachche ko samjhao

Ek busy doorway imagine karo aur tum count karo ki har second kitne log andar se guzarte hain. Electric current bilkul wahi hai, lekin logon ki jagah tiny electric charges hain. "1 ampere" ka matlab hai "1 coulomb-sized bucket of charge har second guzarta hai." Agar har second zyada charge march karta hai, toh current badi hai. Simple hai — bus counting hai!

Active recall

Electric current kya hai?

Ek point se electric charge ke flow ki rate,

I = Δ Q /Δ t

Ampere define karo.

Ek coulomb charge ka ek point se per second guzarna:

1 A = 1 C/s

SI base unit kaun si hai, current ya charge?

Ampere (current); charge derived hai as

1 C = 1 A\cdots

Current ka instantaneous form?

I = \frac{d Q}{d t}

— charge–time graph ka slope.

Steady current ke liye charge formula?

Q = I t

(sirf tab valid jab

I

constant ho).

Agar current vary kare toh charge kaise nikaalein?

Q = \int I d t

I

–

t

graph ke neeche ka area.

Microscopic current equation?

I = n q A v_{d}

(carrier density × charge × area × drift speed).

Conventional current ka direction electrons ke relative?

Conventional current electron drift ke opposite flow karta hai (+ se –).

1 C mein kitne electrons hain?

N = 1/ (1.6 \times 1 0^{- 19}) \approx 6.25 \times 1 0^{18}

Agar electrons slow drift karte hain toh lights instantly kyun jalti hain?

Electric field/signal light speed ke paas propagate karta hai, saare electrons ko ek saath nudge karta hai.