Power, Energy, and Efficiency

Power, $P=VI$

As, $1kW=1000W ; 1hr=3600s$
$1kWh=1000Wh=3600000=3.6\times10^6Ws=3.6\times10^6J$

1 horse power is equal to 746 watts.

1 watt is defined as 1 joule/second.

So $1kW = 1000W$, and $1 hour =60 \times 60 seconds $

So $1kWh = 3600kWs = 3,600,000Ws = 3,600,000J$

$1kWh=3.6*{{10}^{6}}J$

Watt is defined as joule per second. Kilowatt is $10^3$joule per second and kwh is kilowatt hour $10^3\times60\times60$ 

1 kWh is equal to 3.6 $\times$ 10$^{6}$

calorie (cal) is the energy needed to increase 1 gram of water by 1°C at a pressure of 1 atmosphere.

One kilowatt-hour is the energy consumed by a 1 kW device in 1 hour. Since 1 kW = 1000 J/s and 1 hour = 3600 s, 1 kWh = 1000 * 3600 = 3.6 * 10^6 Joules.

Horsepower (hp) is a unit of measurement of power (the rate at which work is done).A power level of 1 hp is approximately equivalent to $746$ watt (W) or $0.746$ kilowatt (kW).

The electrical unit for the electricity of home is used as kilowatt hour (kWh). Here the cost of 1 kWh electricity is Rs 150.  

The kilowatt hour is a unit of energy equal to 3.6 megajoules. If the energy is being transmitted or used at a constant rate over a period of time, the total energy in kilowatt hours is the power in kilowatts multiplied by the time in hours.

$1Wh=1W\times{1h}$

$=1{J}.{s}^{-1}\times{3600}s$

$=3600J=3.6kJ$

$1kWh=1kW\times{1h}$

$=1000{J}.{s}^{-1}\times{3600}s$

$=3.6\times{10}^{6}J=3.6MJ$

$1\ cal=4.2\ J$

unit of energy is joule.