Calculate electrical power (P = VI, P = I²R)

1.1.7 · Hardware › Electricity & Charge Basics

WHAT hai electrical power?

WHY kare hum parwah (Hardware angle): Har component ki ek power rating hoti hai. 0.25 W par rated ek resistor literally jal jaayega agar aap uske through zyada power push karo. Power = heat = woh cheez jo aapki PSU ko pighlati hai, CPU ko throttle karti hai, aur battery ko drain karti hai. $P$ jaanna aapko heat aur energy use batata hai.

HOW derive karein $P = V I$ ko first principles se

Definitions se shuru karo — yaad mat karo, build karo.

Voltage = energy per unit charge: $V = \frac{E}{Q} \Rightarrow E = V Q$ . Yeh step kyun? Voltage ka matlab literally hai "har coulomb ko diye gaye joules," toh total energy hai voltage times kitna charge aapne move kiya.
Current = charge per unit time: $I = \frac{Q}{t} \Rightarrow Q = I t$ . Yeh step kyun? Current batata hai kitni tezi se charge flow karta hai, toh charge = current × time.
Power $P = \frac{E}{t}$ mein substitute karo: $P = \frac{E}{t} = \frac{V Q}{t} = \frac{V ( I t )}{t} = V I$ Yeh step kyun? $t$ cancel ho jaata hai — energy per second directly voltage × current ban jaati hai.

HOW paayein $P = I^{2} R$ aur $P = V^{2} / R$

Hamare paas pehle se $P = V I$ hai. Ab laao Ohm's law: $V = I R$ .

$V$ replace karo: $P = V I = (I R) I = I^{2} R$

$I$ replace karo (kyunki $I = V / R$ ): $P = V I = V \cdot \frac{V}{R} = \frac{V ^{2}}{R}$

Figure — Calculate electrical power (P = VI, P = I²R)

Worked examples

Common mistakes (Steel-man + fix)

Recall Feynman: ek 12-saal ke bachche ko samjhao

Ek water slide imagine karo. Voltage hai slide kitni ऊchi hai (kitna drop hai). Current is how many kids slide down each second. Power is how much total whee! energy happens per second — ek ऊchi slide pe bahut saare bachche bahut power dete hain. Agar slide rough hai (resistance), bachche usse ragadte hain aur woh garam ho jaati hai — woh heat hai $I^{2} R$ , aur yeh bahut tezi se badhti hai agar zyada bachche aate hain, kyunki woh ek doosre ko slow karte hain aur zyada press karte hain.

Flashcards

Power ki SI unit kya hai aur yeh kiske barabar hai?

The watt (W);

1 W = 1 J/s

P = V I

ko definitions se derive karo.

V = E / Q

aur

I = Q / t

;

P = E / t = V Q / t = V (I t) / t = V I

P = V I

P = I^{2} R

kaise nikaalte hain?

Ohm's law

V = I R

substitute karo:

P = (I R) I = I^{2} R

P = V^{2} / R

kaise nikaalte hain?

I = V / R

P = V I

mein substitute karo:

P = V (V / R) = V^{2} / R

Agar current aur resistance pata ho lekin voltage nahi, toh kaun sa formula?

P = I^{2} R

Agar voltage aur resistance pata ho lekin current nahi, toh kaun sa formula?

P = V^{2} / R

Agar ek fixed resistor mein current double ho jaaye, toh power mein kya change aata hai?

Yeh chaar guna (×4) ho jaata hai, kyunki

P \propto I^{2}

Ek 5 V, 2 A charger kitni power deliver karta hai?

P = V I = 10 W

Ek 60 W device se 2 hours mein energy (joules mein)?

E = P t = 60 \times 7200 = 432, 000 J

Thick, low-resistance wire heat loss kyun reduce karti hai?

Lower

R

matlab same current ke liye lower

I^{2} R

heat.

Connections

Ohm's Law (V = IR) — woh bridge jo $P = V I$ ko $I^{2} R$ aur $V^{2} / R$ mein turn karta hai.
Voltage and Potential Difference — charge per energy, $V Q$ term ka source.
Electric Current — charge per time, $I t$ term ka source.
Energy and the Joule — $E = P t$ , billing (kWh) aur battery capacity.
Resistors and Power Ratings — kyun ek 0.25 W resistor jal jaata hai.
Heat Dissipation and Cooling — CPUs, wires, PSUs mein $I^{2} R$ losses.