Series and parallel resistance — Hinglish notes

1.8.17 · Physics › Electromagnetism

"Equivalent resistance" kya hota hai?

Hum sab kuch sirf do laws se derive karte hain:

Ohm's law: $V = I R$ (WHAT: ek resistor ke across voltage = current × uski resistance).
Kirchhoff's laws:
- KVL (loop): ek loop mein voltages ka sum zero hota hai → ek single line mein, applied $V$ resistors mein split hoti hai.
- KCL (node): current in = current out → ek junction par currents split/recombine hoti hain.

Series — scratch se derivation

Setup: $R_{1}, R_{2}, \dots, R_{n}$ ek single line mein, chain ke across total voltage $V$ , current $I$ .

HOW (derive): Har ek ke across voltage (Ohm se): $V_{k} = I R_{k}$ . KVL se applied voltage drops ke sum ke barabar hai: $V = V_{1} + V_{2} + \dots + V_{n} = I R_{1} + I R_{2} + \dots + I R_{n} = I \sum_{k} R_{k}$ Kyunki $R_{e q} = V / I$ : $R_{ser i es} = R_{1} + R_{2} + \dots + R_{n}$

Parallel — scratch se derivation

Setup: $R_{1}, \dots, R_{n}$ sab node A aur node B ke beech connected hain. Common voltage $V$ , total current $I$ jo A mein enter karti hai.

HOW (derive): Har ek se current (Ohm se): $I_{k} = V / R_{k}$ . KCL se total current branches mein split hoti hai: $I = I_{1} + I_{2} + \dots + I_{n} = \frac{V}{R _{1}} + \frac{V}{R _{2}} + \dots + \frac{V}{R _{n}} = V \sum_{k} \frac{1}{R _{k}}$ Kyunki $\frac{1}{R _{e q}} = \frac{I}{V}$ : $\frac{1}{R _{p a r a l l e l}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots + \frac{1}{R _{n}}$

Worked examples

Common mistakes (Steel-man + fix)

Recall Feynman: ek 12-saal ke bachche ko explain karo

Paani ke pipes socho. Series = ek lamba pipe jisme kai tange choke ek ke baad ek hain; paani ko har choke se squeeze hona padta hai, toh chokes ki "difficulty" pile up hoti hai — total mushkil ho jaata hai. Parallel = same paani ek aise jagah pahunchta hai jahaan woh kai side-by-side pipes mein split ho sakta hai; zyada pipes matlab paani overall asaan se bahta hai, toh total difficulty sabse asaan single pipe se bhi neeche aa jaati hai. Series chain mein har jagah same paani-per-second; har side-by-side pipe ke across same paani-pressure.

Flashcards

Series mein, har resistor ke liye kaun si quantity identical hoti hai?

Current

I

(single path, KCL).

Parallel mein, har resistor ke liye kaun si quantity identical hoti hai?

Voltage

V

(same do nodes).

Series equivalent resistance formula?

R_{e q} = R_{1} + R_{2} + \dots + R_{n}

Parallel equivalent resistance formula?

\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \dots + \frac{1}{R _{n}}

Do-resistor parallel shortcut?

R_{e q} = \frac{R _{1} R _{2}}{R _{1} + R _{2}}

(product over sum).

Kya series

R_{e q}

har resistor se bada hota hai ya chota?

Kisi bhi single se bada.

Kya parallel

R_{e q}

har resistor se bada hota hai ya chota?

Sabse chote se bhi chota.

n

equal resistors

R

parallel mein kya dete hain?

R / n

Parallel mein, kaun sa resistor zyada current leta hai?

Chota resistance (

I_{k} = V / R_{k}

Ye formulas kaun si do laws se derive hoti hain?

Ohm's law + Kirchhoff's (KVL for series, KCL for parallel).

Series chain mein voltages kaise relate karte hain?

Woh applied voltage mein add hote hain (KVL).

Parallel junction par currents kaise relate karti hain?

Woh total current mein add hoti hain (KCL).

Connections

Ohm's Law — woh $V = I R$ jo har step par use hoti hai.
Kirchhoff's Laws — KVL (series) aur KCL (parallel) in rules ka asli source hain.
Resistivity and Resistance — jahaan se ek single $R$ aata hai ( $R = ρ L / A$ ).
EMF and Internal Resistance — internal resistance battery ke saath series mein hoti hai.
Wheatstone Bridge — aisi networks jo purely series ya parallel nahi hain.
Power in Circuits — $P = I^{2} R = V^{2} / R$ combination mein distribute hoti hai.