Apply electric power formulas
Scenario
Dukaan par aap `9 W` ka LED bulb maangte hain.
Is `9 W` ka actual physics mein matlab kya hota hai?
Mental model
Power matlab speed of consuming energy. Jiski power zyada, wo utni tezi se bijli khaayega.
Rate at which electric energy is consumed is called electric power. `9 W` bulb ka matlab hai wo har second `9 J` energy use kar raha hai.
Explanation
Electric power ko `P` se likhte hain. Iska basic formula `P = V I` hai, jahan `V` voltage hai aur `I` current hai.
Agar humein `V` nahi pata aur `R` pata hai, toh Ohm's law (`V = I R`) use karke:
P = (I R) * I
P = I^2 R
Yeh formula tab best hai jab current (`I`) aur resistance (`R`) pata ho (jaise series circuits mein).
Aur agar humein `I` nahi pata, toh `I = V / R` use karke:
P = V * (V / R)
P = V^2 / R
Yeh formula appliances ke liye bahut useful hai kyunki gharon mein `V` (`220 V`) constant (parallel) rehta hai.
Power ki SI unit Watt (`W`) hai. Commercial bijli ka bill nikalne ke liye unit 'kilowatt-hour' (`kWh`) hoti hai. `1 kWh` ka matlab hai `1 kW` (`1000 W`) ka appliance `1` ghante tak chala. `1 kWh = 3.6 x 10^6 J`.
Worked example
Problem: An electric bulb is connected to a `220 V` generator. The current is `0.50 A`. What is the power of the bulb?
- `V` aur `I` dono directly diye gaye hain.
- Power ka basic formula use karte hain.
- Values multiply karte hain.
Answer: `110 W`
Problem: An electric refrigerator rated `400 W` operates `8` hours/day. What is the cost of the energy to operate it for `30` days at Rs `3.00` per `kWh`?
- Total energy `E = P t` nikalte hain. Power ko `kW` mein aur time ko hours mein rakhte hain.
- Total time for `30` days calculate karte hain.
- Energy `kWh` mein aayegi.
- Cost nikalne ke liye rate se multiply karte hain.
Answer: Rs `288`
Key points
- Three Formulas: `P = V I`, `P = I^2 R`, and `P = V^2 / R`.
- Commercial Unit: `1 kWh = 3.6 x 10^6 J`. This is `1` 'Unit' on your electricity bill.
Common mistakes
- Confusing W with kWh: Watt (`W`) Power ki unit hai, aur Kilowatt-hour (`kWh`) Energy ki. Inhe mix mat karna.
- Using wrong time unit for kWh: `kWh` calculate karte time, time hamesha hours mein hona chahiye, seconds mein nahi.
Recall questions
- What is the SI unit of power?
- `1 kWh` is equal to how many Joules?
- What is the formula for electric power in terms of resistance and current?
Questions & answers
Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be?
`1:4`
Approach: Use `P = V^2 / R`. In series, `R_s = 2 R`. In parallel, `R_p = R / 2`. Ratio = `(V^2 / 2 R) / (V^2 / (R / 2)) = 1/4`.
An electric heater is rated `1500 W`. How much energy does it use in `10` hours?
`15 kWh`
Approach: Energy = Power * time = `1.5 kW * 10 h` = `15 kWh`.
Continue learning
Previous: State Ohm's Law