RL circuit — growth and decay of current: Question bank

1.8.29 · D5 · Physics › Electromagnetism › RL circuit — growth and decay of current

Shuru karne se pehle, har symbol ki ek-line reminder taaki kuch assume na ho:

$ε$ = battery EMF (woh "push", volts mein).
$R$ = resistance (ohms, $Ω$ ); $L$ = inductance (henry, H).
$I$ = current (amps); $\frac{d I}{d t}$ = current kitni tezi se change ho rahi hai.
$τ = L / R$ = time constant (seconds) — circuit ki natural clock.
$V_{L} = L d I / d t$ = inductor ke across voltage.

Why questions

Why does the inductor voltage

V_{L}

fall during growth while the resistor voltage rises?

Dono ko

ε

mein sum karna hai (KVL). Shuruaat mein inductor push hogg karta hai (

V_{L} \approx ε

, current tiny); jaise current badhti hai,

I R

barta hai aur

V_{L} = ε e^{- t / τ}

total ko

ε

par rakhne ke liye shrink hota hai.

Why is the RL story called "an exponential approach to equilibrium"?

Change ki rate proportional hai kitna target se door ho (

d I / d t \propto ε - I R

). Jab bhi change-rate remaining distance ke proportional ho, solution ek exponential hota hai — jaise RC charging.

Why does a large

L

make the circuit "sluggish"?

Bada

L

matlab diye gaye

d I / d t

ke liye bada back-EMF, toh same current change ko zyada fight milta hai. Yeh electromagnetic inertia hai — current ka version ek heavy mass ki tarah jo acceleration resist karta hai.

Why can current keep flowing after the battery is removed?

Inductor ne apni magnetic field mein energy

\frac{1}{2} L I_{0}^{2}

store ki thi. Faraday+Lenz ke anusaar, jaise woh field collapse hota hai yeh ek EMF drive karta hai jo current maintain karta hai, jo phir

R

se decay karta hai.

Why do we check units to remember

τ = L / R

and not

R / L

τ

seconds mein hona chahiye.

[L] / [R] = H /Ω = (V\cdots/A) / (V/A) = s

✓, jabki

R / L

1/ s

deta hai — ek frequency, time nahi. Units ambiguity instantly settle kar deti hai.

Why is the inductor the "opposite" of the capacitor at

t = 0

Ek capacitor short se shuru hota hai (current surge allow karta hai, voltage jump block karta hai), ek inductor open se shuru hota hai (current surge block karta hai, voltage jump allow karta hai). Yeh roles swap karte hain kyunki inductors current change resist karte hain jabki capacitors voltage change resist karte hain.

Edge cases

What happens to

τ

and the current if

L \to 0

(ideal wire, no inductor)?

τ = L / R \to 0

: smoothing vanish ho jaata hai aur current instantly

ε / R

tak jump karta hai. Circuit reduce ho jaata hai ek pure resistor mein jo plain Ohm's law follow karta hai.

What happens if

R \to 0

during decay (a superconducting-like short)?

τ = L / R \to \infty

: decay kabhi khatam nahi hoti — koi resistor nahi energy dissipate karne ke liye, current

I_{0}

essentially forever circulate karta hai. Yeh idealized "persistent current" limit hai.

ε = 0

from the start (no battery ever connected), what is the current?

Har time par zero. Growth formula deta hai

I = (0/ R) (1 - e^{- t / τ}) = 0

; koi push nahi aur koi stored energy nahi toh current drive karne ke liye kuch nahi.

At exactly

t = 0

in growth, what are

I

\frac{d I}{d t}

, and

V_{L}

I = 0

(koi jump nahi),

\frac{d I}{d t} = ε / L

(yahan sabse steep), aur

V_{L} = ε

(inductor poora EMF leta hai kyunki

I R = 0

t \to \infty

in growth, what happens to

\frac{d I}{d t}

and

V_{L}

Dono

\to 0

: current

ε / R

par level off hoti hai, toh change karna band kar deti hai, aur inductor voltage

L d I / d t

zero par collapse ho jaata hai — inductor ab plain wire ki tarah behave karta hai.

If you connect two identical inductors in series, how does

τ

change?

Series inductances add hote hain (

L \to 2 L

), toh

τ = 2 L / R

double ho jaata hai — circuit do guna sluggish ho jaata hai, haalaanki final current

ε / R

unchanged rehti hai.

Recall One-line self-test

Growth $τ$ par 63% tak rise karti hai; decay $τ$ par 37% tak girta hai; inductor = shuru mein Open, end mein wire; $τ = L / R$ (units force karte hain). ::: Agar tum sab chaar reasons ke saath memory se bol sako, tumne trap set clear kar liya.

Connections

Inductance and self-induction — $L d I / d t$ opposition kyun exist karta hai.
Lenz's law — upar har "why" mein back-EMF ka sign.
Energy stored in a magnetic field — woh $\frac{1}{2} L I^{2}$ jo decay ko power karta hai.
Kirchhoff's voltage law — sign-error traps ke peeche loop rule.
RC circuit — charging and discharging — woh dual jiska confusion $τ$ mix-ups cause karta hai.

Question bank — RL circuit — growth and decay of current

True or false — justify

Spot the error

Why questions

Edge cases

Connections