Chapter 11 · Question 10

Define electric power. Derive the different forms of the power formula, and explain the commercial unit of electrical energy (kWh).

Q10

Define electric power. Derive the different forms of the power formula, and explain the commercial unit of electrical energy (kWh).

Answer Revealed

Direct Answer:

Electric power is the rate at which electric work is done or electrical energy is consumed. Power

P = W/t = VI

. Using Ohm's law (

V = IR

), this can also be written as

P = I^2 R

and

P = V^2 / R

. The commercial unit of electrical energy is the kilowatt-hour (kWh), where

1\ \text{kWh} = 3.6 \times 10^6\ \text{J}

— it is the energy consumed when a device of 1 kW power operates for 1 hour.

Simple Explanation

Power tells you how fast an appliance uses energy — a 100 W bulb uses energy faster than a 15 W bulb. The three forms of the power formula (

P = VI

P = I^2 R

P = V^2/R

) all say the same thing in different ways. Your electricity bill uses kilowatt-hours (kWh), also called 'units'. One kWh means running a 1000 W heater for one hour, which equals 3.6 million joules.

Exam-Ready Structure

Electric power and the commercial unit of energy are essential for understanding electricity consumption and billing: 1. Definition of electric power: Power (

P

) is the rate at which electric work is done or electrical energy is consumed/dissipated in a circuit.

P = \text{Work done} / \text{Time} = W / t

. Since

W = V Q

and current

I = Q / t

, we get

P = V I

. The SI unit of power is the watt (W), where

1\ \text{W} = 1\ \text{V} \times 1\ \text{A}

. Larger units are kilowatt (

1\ \text{kW} = 1000\ \text{W}

) and megawatt (

1\ \text{MW} = 10^6\ \text{W}

). 2. Different forms of the power formula: Using Ohm's law (

V = I R

), the basic formula

P = V I

can be rewritten in two other useful forms: (a)

P = V I = I R \times I = I^2 R

. This form is convenient when current and resistance are known. (b)

P = V I = V \times (V / R) = V^2 / R

. This form is convenient when voltage and resistance are known. All three forms are equivalent and give the same power value. 3. Rating of appliances: Every electrical appliance has a power rating marked on it. For example, a bulb marked 60 W, 220 V means it consumes 60 W of power when operated at 220 V. 4. Commercial unit — kilowatt-hour (kWh): The SI unit of energy (joule) is too small for commercial billing. The commercial unit is the kilowatt-hour (1 kWh). 1 kWh is the electrical energy consumed when an appliance of power 1000 W (1 kW) operates for 1 hour. 5. Relationship: Energy = Power

\times

Time.

1\ \text{kWh} = 1\ \text{kW} \times 1\ \text{h} = 1000\ \text{W} \times 3600\ \text{s} = 3.6 \times 10^6\ \text{J}

. This is why 1 kWh is also called 'one unit' of electricity on your electricity bill. 6. Example: A 100 W bulb used for 10 hours consumes

100\ \text{W} \times 10\ \text{h} = 1000\ \text{Wh} = 1\ \text{kWh} = 1

unit.

Key Points

Electric power $P = VI = I^2 R = V^2 / R$ (three equivalent forms)
SI unit of power is watt (W); $1\ \text{W} = 1\ \text{V} \times 1\ \text{A}$
Larger power unit: $1\ \text{kW} = 1000\ \text{W}$
Commercial unit: kilowatt-hour (kWh), also called one 'unit'
$1\ \text{kWh} = 3.6 \times 10^6\ \text{J}$ (energy consumed by a 1 kW device in 1 hour)

Common Mistakes

Saying kWh is a unit of power (kWh is a unit of energy; kW is power)
Forgetting the time factor while calculating energy or heat (use E = P t or H = I^2 R t, not just power alone)

Define electric power. Derive the different forms of the power formula, and explain the commercial unit of electrical energy (kWh).