Electrical Energy and Power: Definition, Formulas and Examples

Electrical power tells us how quickly an electrical device transfers or converts energy. Electrical energy tells us how much energy is transferred over a period of time.

For example, a 1000 W heater transfers energy faster than a 100 W lamp when both operate at their rated power. This lesson explains the formulas, units and everyday applications of electrical energy and power.

In this lesson

1. What is electric power?

Electric power is the rate at which electrical energy is supplied to a circuit or converted into another form, such as light, heat, sound or mechanical motion. A device that transfers more energy each second has a higher power rating.

In a DC circuit, the electrical power delivered to a component is calculated by multiplying the voltage across it by the current through it:

P = VI

where:

P = electrical power in watts (W)

V = potential difference in volts (V)

I = current in amperes (A)

For a resistor obeying Ohm's law, \(V=IR\), the same power can also be calculated using these formulas:

When current and resistance are known

P = I²R

When voltage and resistance are known

P = V²/R

These expressions are equivalent for an ohmic resistor. Choose the one that uses the quantities provided in the question.

2. Interactive SVG: Explore power in an electric circuit

Change the battery voltage and resistance below. The diagram and readings update automatically. Watch how the current and power change when you adjust either value.

Interactive battery, resistor and lamp circuit A closed DC circuit with a battery, a resistor and a light bulb. Adjust the voltage and resistance to see the calculated current and power. + − Battery 12 V Resistor 6 Ω Lamp I DC circuit Illustration of a simplified resistive load
Current (I) 2.00 A I = V/R
Power (P) 24.0 W P = VI
Energy in 10 minutes 14,400 J E = Pt

Relative power display

This is an idealised DC circuit. The calculated power is the electrical power dissipated by the resistive load. The lamp graphic is illustrative, not a detailed filament model.

3. What is electrical energy?

Electrical energy is the amount of energy transferred when electric charge moves through a potential difference. It may be converted into heat in a heater, light in a lamp, sound in a speaker or mechanical motion in a motor.

Since power is the energy transferred per unit time, electrical energy can be calculated by multiplying power by operating time:

E = Pt

For a constant voltage and current in a DC circuit:

E = VIt

Here, E is energy in joules (J), P is power in watts (W), and t is time in seconds (s).

Remember: Power describes how fast energy is transferred. Energy describes the total amount transferred during a period of time.

How does operating time affect energy use?

If a device operates at constant power, doubling its operating time doubles the energy it consumes. For example, a 100 W device operating for 2 hours uses twice the energy it uses in 1 hour.

4. Units of electrical power and energy

Quantity Unit Meaning
Power Watt (W) One joule of energy transferred per second.
Power Kilowatt (kW) 1 kW = 1000 W.
Energy Joule (J) SI unit of energy; 1 J = 1 W × 1 s.
Electrical energy Kilowatt-hour (kWh) Energy used by a 1 kW device in 1 hour.
1 kWh = 3.6 × 10⁶ J

1 kWh = 1000 W × 3600 s = 3,600,000 J.

Electricity meters commonly record household energy use in kilowatt-hours. A unit on an electricity bill generally means 1 kWh, not 1 kW.

Power ratings of common devices

LED lamp

A lamp rated at 10 W uses 10 joules of energy per second when operating at its rated power.

Ceiling fan

A fan rated at 75 W uses 0.075 kWh when it runs for one hour at that power.

Electric heater

A 1000 W heater operating for one hour uses 1 kWh of energy at its rated power.

Electric motor

Electrical input power can be greater than useful mechanical output power because real motors have losses.

5. Electrical power and energy calculator

Enter voltage, current and operating time to estimate power and electrical energy for a DC circuit with constant voltage and current.

Calculate power and energy

Enter the values and select Calculate.

6. Solved examples of electrical energy and power

Example 1: Calculate electric power

Question: A device operates at 12 V and draws a current of 2 A. Find its electrical power.

Given: V = 12 V, I = 2 A

P = VI

P = 12 × 2

P = 24 W

Answer: The device's electrical power is 24 W.

Example 2: Calculate electrical energy in joules

Question: A 100 W lamp operates for 5 minutes. Find the energy transferred.

Given: P = 100 W, t = 5 × 60 = 300 s

E = Pt

E = 100 × 300

E = 30,000 J

Answer: The energy transferred is 30,000 J.

Example 3: Calculate energy in kilowatt-hours

Question: A 1.5 kW heater operates for 2 hours. How much electrical energy does it use?

E = Pt

E = 1.5 kW × 2 h

E = 3 kWh

Answer: The heater uses 3 kWh, equivalent to 10.8 million joules.

Example 4: Calculate power using resistance

Question: A 6 Ω resistor is connected across a 12 V DC supply. Calculate the power dissipated.

Given: V = 12 V, R = 6 Ω

P = V²/R

P = 12²/6 = 144/6

P = 24 W

Answer: The resistor dissipates 24 W under these ideal conditions.

7. Why are electrical energy and power important?

  • Electricity bills: Energy consumption in kWh helps calculate the cost of operating household appliances.
  • Appliance selection: Power ratings help compare the energy-transfer rate of devices.
  • Electrical safety: Power and current ratings help engineers select appropriate components and wiring.
  • Battery life: Energy capacity and the power demanded by a device help estimate operating time.
  • Energy efficiency: Comparing useful output with energy input helps identify losses in motors, lamps and other equipment.
  • Heating: Electrical energy can be converted into heat in resistive elements.

Quick revision

Electric power:

P = VI

Power in an ohmic resistor:

P = I²R = V²/R

Electrical energy:

E = Pt = VIt

Unit conversions:

1 kW = 1000 W 1 kWh = 3.6 × 10⁶ J

8. Frequently asked questions

What is electric power?

Electric power is the rate at which electrical energy is transferred or converted. Its SI unit is the watt (W).

What is the formula for electrical power?

For a DC circuit, P = VI. For an ohmic resistor, P = I²R and P = V²/R can also be used.

What is the difference between electrical energy and power?

Power tells us how quickly energy is transferred. Electrical energy is the total amount transferred over a period of time.

How many watts are in one kilowatt?

One kilowatt is equal to 1000 watts.

What is one kilowatt-hour?

One kilowatt-hour is the energy used by a 1 kW device operating for one hour. It equals 3.6 million joules.

Does a higher-power appliance always use more energy?

Not necessarily. Energy use depends on both power and operating time. A higher-power appliance can use less total energy if it runs for a sufficiently shorter period.

Can P = VI be used for AC circuits?

For a DC circuit, P = VI gives electrical power. For sinusoidal AC, average real power is P = VrmsIrms cos φ, where φ is the phase angle between voltage and current. In a purely resistive AC load, the power factor cos φ is 1.

For related lessons, study Ohm's law, electric current and electric current in conductors.