Calculate heat generated by current
Scenario
Phone ko lagatar charge karne par wo garam kyu ho jata hai?
Current guzarne par heat paida hoti hai. Ye heat kitni hogi, iska formula kya hai?
Mental model
Electric friction heat paida karta hai.
Jab electrons wire (resistor) mein bhaagte hain, toh wo atoms se takrate hain. Is takkar (resistance) ki wajah se kinetic energy heat mein badal jati hai.
Explanation
Is process ko heating effect of electric current kehte hain. Iska mathematically study James Prescott Joule ne kiya tha.
Joule's law of heating kehta hai ki heat paida hona (`H`) teen cheezon par depend karta hai: Current ka square (`I^2`), Resistance (`R`), aur Time (`t`) jiske liye current baha.
Formula hai `H = I^2 * R * t`. Heat ek tarah ki energy hai, isliye iski SI unit Joule (`J`) hoti hai. Formula use karte waqt time humesha seconds mein hona chahiye.
Ye effect humare liye nuksaan-dayak bhi hai (phone ka garam hona) aur faydemand bhi. Electric heater, iron, toaster, aur bulb sab is principle par kaam karte hain. Electric fuse bhi isi wajah se melt hokar circuit todta hai jab current limit se zyada badh jaye.
Worked example
Problem: `100 J` of heat is produced each second in a `4 ohm` resistance. Find the potential difference across the resistor.
- Given values likhte hain.
- Joule's law `H = I^2 R t` se current nikalte hain.
- Phir Ohm's law `V = IR` lagakar voltage nikalte hain.
Answer: 20 V
Problem: Compute the heat generated while transferring `96000 coulomb` of charge in one hour through a potential difference of `50 V`.
- Pehle time ko seconds mein convert karte hain.
- Current `I = Q/t` use karke nikalte hain.
- Ohm's law `R = V/I` se resistance nikalte hain.
- `H = V I t` ka bhi sidha istemaal kar sakte hain, jo aur asaan hai (`H = W = VQ`).
Answer: 4.8 * 10^6 J
Key points
- Joule's Law of Heating: `H = I^2 * R * t`.
- Dependencies: Heat is directly proportional to square of current, resistance, and time.
Common mistakes
- Forgetting to square the current: `H = I^2 * R * t` ki jagah jaldi mein `H = I * R * t` likh dete hain. `I` ka square karna zaruri hai.
Recall questions
- What is the SI unit of heat generated in a circuit?
- State the formula for Joule's law of heating.
- What is Joule's Law of Heating equation?
Questions & answers
Why does the cord of an electric heater not glow while the heating element does?
The heating element has very high resistance, so it produces a lot of heat (H = I^2Rt) and glows. The cord has low resistance (copper), so it produces negligible heat.
Approach: Compare their resistances using Joule's law.
100 J of heat is produced each second in a 4Ω resistance. Find the potential difference across the resistor.
20 V
Approach: H = V²t/R => 100 = V²(1)/4 => V² = 400 => V = 20 V.
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