1.1.5
Intuition Ek-sentence wala ideaResistance measure karta hai ki koi material electric current ke flow ko kitna oppose karta hai . Same voltage ko ek "harder" path ke across push karo toh kam current milega — us path mein zyada resistance hai.
Resistance R voltage aur us se guzarne wale current ka ratio hai:
R = I V ohm , symbol Ω
Kisi component ka resistance 1 ohm hota hai jab 1 volt ka potential difference us mein se exactly 1 ampere current drive karta hai.
1 Ω = 1 A 1 V
Hum resistance ko aisa define kyun karte hain? Kyunki jab engineers ne metal wires ke saath experiment kiya, unhone notice kiya ki ek fixed wire ke liye, voltage double karne par current double ho jaata tha, voltage triple karne par current triple — ratio V / I
Hum R = V / I
Toh ohm ek derived unit hai: 1 Ω = 1 V/A = 1 C/s J/C = 1 C 2 J ⋅ s
Upar wala graph I–V characteristic hai. Ek ohmic resistor ke liye yeh origin se guzarne wali ek straight line hoti hai; iska slope 1/ R , isliye steeper line ka matlab hai choti resistance.
Intuition Slope vs resistance (dual coding)Ek I V = I / V = 1/ R
Worked example Example 1 — Resistance nikaloEk 12 V battery ek heating element se 3 A push karti hai. R R = I V = 3 A 12 V = 4 Ω Yeh step kyun? Hum directly definition use karte hain — resistance bas voltage divided by current hai.
Worked example Example 2 — Current nikaloEk 220 V supply ko 1100 Ω I R = V / I ⇒ I = V / R I = 1100 Ω 220 V = 0.2 A Yeh step kyun? Hum algebraically usi ek equation ko unknown (I
Worked example Example 3 — Voltage nikalo8 Ω V = I R = 0.5 A × 8 Ω = 4 V Yeh step kyun? Wapas multiply karne se woh "push" milta hai jo us resistance se us current ke liye chahiye.
Worked example Example 4 — Forecast-then-verifyForecast: Agar main resistance half kar doon lekin voltage same rakhuun, toh current ka kya hoga?
Verify: I = V / R R → R /2 I → V / ( R /2 ) = 2 V / R double ho jaata hai . ✔ Kam resistance ⇒ zyada current, intuition se match karta hai.
Common mistake "Zyada voltage matlab zyada resistance."Kyun sahi lagta hai: Bada voltage "zyada effort" jaisa lagta hai, toh tum ise ek harder path se associate karte ho.
Fix: Resistance ek component ki property hai, voltage ki nahi. V I ratio V / I = R
Common mistake "Ohm aur volt same hain kyunki dono electricity measure karte hain."Kyun sahi lagta hai: Dono V = I R Fix: Volt = energy per charge (the push). Ohm = push per unit resulting flow (the opposition). Alag physical quantities, alag units.
Common mistake I–V slope ko resistance hi samajh lena.Kyun sahi lagta hai: Slope graph ka "main number" jaisa "dikhta" hai.
Fix: Slope = I / V = 1/ R reciprocal hai. R 1/ slope V / I
Recall Feynman: ek 12-saal ke bachche ko samjhaoSocho paani ek pipe mein beh raha hai. Voltage hai ki tum paani ko kitna zyada push karte ho. Current hai ki actual mein kitna paani per second bahar aata hai. Resistance hai ki pipe kitni narrow ya clogged hai. Ek thin, clogged pipe (high resistance) bade push ke bawajood sirf thoda sa paani aane deti hai. Ek wide clean pipe (low resistance) chhote push se paani ugal deti hai. Resistance = "pipe kitna fight back karta hai," aur hum ise ohms mein measure karte hain: 1 ohm matlab 1 volt ka push exactly 1 amp ka flow deta hai.
Mnemonic Triangle yaad rakhoEk triangle banao: V upar, I aur R neeche.
V V = I × R I I = V / R R R = V / I "Very Important Rule." (V I R
Ek sentence mein resistance kya hai? Woh opposition jo ek component electric current ko offer karta hai, voltage divided by current ke barabar (R = V / I
Resistance ki SI unit aur uska symbol kya hai? Ohm, symbol Ω
Ek ohm define karo. Woh resistance jab 1 volt exactly 1 ampere component se drive karta hai (1 Ω = 1 V /1 A
Current nikalne ke liye R = V / I I = V / R
Voltage nikalne ke liye R = V / I V = I R
Ek I-vs-V graph par slope kya equal hota hai? Resistance ka reciprocal, 1/ R
Agar voltage fixed rahe aur resistance half ho jaaye, toh current ka kya hoga? Yeh double ho jaata hai (I = V / R
Ohm ko base units mein express karo. 1 Ω = 1 J⋅s/C 2
Kya resistance component ki property hai ya applied voltage ki? Component ki (uska material, size, temperature) — applied voltage ki nahi.
Ek 12 V supply 4 A deti hai. R kya hai? 12/4 = 3 Ω
Ohm's law V proportional to I
