Build and analyze a voltage divider — Hinglish notes

1.2.5 · Hardware › Circuit Analysis Fundamentals

Yeh hai kya?

Figure — Build and analyze a voltage divider

Isse scratch se derive karo (bare formula kabhi mat memorize karo)

KAISE — Ohm's law + series rules se first principles use karke.

Step 1 — Series resistance. $R_{1}$ aur $R_{2}$ same current $I$ carry karte hain (unke beech koi branch nahi). Total resistance: $R_{t o t a l} = R_{1} + R_{2}$ Yeh step kyun? Series mein sirf ek hi path hota hai, isliye resistances add ho jaate hain.

Step 2 — Ohm's law se current nikalo. $I = \frac{V _{in}}{R _{t o t a l}} = \frac{V _{in}}{R _{1} + R _{2}}$ Yeh step kyun? Poora $V_{in}$ current ko poore loop mein push karta hai.

Step 3 — $R_{2}$ ke across voltage (wahi $V_{o u t}$ hai). Sirf $R_{2}$ par Ohm's law: $V_{o u t} = I \cdot R_{2} = \frac{V _{in}}{R _{1} + R _{2}} \cdot R_{2}$ Yeh step kyun? Output node $R_{2}$ ke across baith ta hai, isliye uski voltage = current × $R_{2}$ .

Step 4 — Saaf karo. $V_{o u t} = V_{in} \cdot \frac{R _{2}}{R _{1} + R _{2}}$ Yeh step kyun? Bas factoring — fraction $\frac{R _{2}}{R _{1} + R _{2}}$ total resistance mein $R_{2}$ ka share hai.

Forecast-then-Verify

Common mistakes (steel-manned)

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

Socho paani ek pahaad se do pipes ke through neeche beh raha hai, ek ke baad ek. Poora pressure upar hota hai. Jab tak paani beech ke junction tak pahunchta hai, pehli pipe mein kuch pressure "use up" ho chuka hota hai. Agar tum beech ke junction par measure karo, toh tumhe pressure ka ek hissa milta hai — chhhoti pipe (mota resistor) zyada use up karta hai. Ek voltage divider electricity ke liye wahi middle-junction tap hai.

Active recall

Voltage divider output formula

V_{o u t} = V_{in} \frac{R _{2}}{R _{1} + R _{2}}

Do voltage drops milke

V_{in}

kyun bante hain?

KVL — ek loop mein total voltage drops source ke barabar hote hain.

Numerator mein kaun sa resistor hota hai, aur kyun?

R_{2}

— kyunki

V_{o u t}

R_{2}

ke across measure hota hai.

V_{o u t}

kya determine karta hai: absolute resistance ya ratio?

Ratio

R_{2} / (R_{1} + R_{2})

R_{2}

ke across load

R_{L}

attach karne ka effect?

R_{2}

ki jagah

R_{2} ∥ R_{L}

daalo;

V_{o u t}

drop ho jaata hai.

Unloaded divider mein current?

I = V_{in} / (R_{1} + R_{2})

, dono resistors mein same.

5 V→3.3 V ke liye ratio

R_{2} / (R_{1} + R_{2})

kya hoga?

3.3/5 = 0.66

Bahut bade divider resistors se kyun bachein?

High output impedance → noise/loading sensitivity.

Connections

Ohm's Law — divider Ohm's law ka do baar application hai.
Series and Parallel Resistors — series mein add hote hain; loading mein parallel aa jaata hai.
Kirchhoff's Voltage Law — drops milke source ke barabar hote hain.
Thevenin Equivalent — ek divider ka output = Thevenin source $V_{o u t}$ with $R_{t h} = R_{1} ∥ R_{2}$ .
Wheatstone Bridge — do dividers compare kiye jaate hain.
Op-amp Buffer — loading problem fix karta hai.