11.8 - Electric Power

Electric power is the rate at which electrical energy is transferred by an electric circuit. It is a measure of how quickly electrical energy is consumed or converted into other forms such as heat, light, or mechanical energy.

Electric power is given by the product of the current flowing through a conductor and the potential difference (voltage) across its ends. The formula for electric power is:

$P = I \times V$

Where:

• P = Electric power (in watts, W)
• I = Current (in amperes, A)
• V = Potential difference (in volts, V)

Since the power is also related to the resistance of the conductor, using Ohm's law ($V = I \times R$), we can derive alternate expressions for power:

$P = I^2 \times R$

Or, using $I = \frac{V}{R}$, we get:

$P = \frac{V^2}{R}$

Thus, electric power can be calculated in three different forms depending on the known quantities (current, voltage, or resistance). The SI unit of electric power is the watt (W), where 1 watt is equal to 1 joule per second (J/s).

Units of Electric Power:

• The unit of electric power is the watt (W), named after James Watt.
• 1 watt = 1 joule/second (J/s).
• Other common units are kilowatt (kW) and megawatt (MW), where 1 kW = 1000 W and 1 MW = 1,000,000 W.

Power in Household Appliances:

In household appliances, electric power is often measured in kilowatts (kW). For example, a 100 W bulb consumes 100 joules of energy per second. When high power consumption is involved (like in motors or heaters), power is typically expressed in kilowatts (kW) or megawatts (MW).

Energy Consumption:

The total energy consumed by an electrical appliance depends on both the power rating and the time it is used. The energy consumed, in joules (J), can be calculated as:

$E = P \times t$

Where:

• E = Energy consumed (in joules, J)
• P = Power (in watts, W)
• t = Time (in seconds, s)

In terms of kilowatt-hours (kWh), the unit commonly used by electricity companies for billing, the energy consumed is:

$E = P \times t \quad (\text{in kWh, if P is in kW and t in hours})$

Efficiency of Electrical Appliances:

In many electrical devices, not all the electrical energy is converted to useful work. Some energy is lost in the form of heat or sound. The efficiency of an appliance is the ratio of the useful energy output to the total energy input, often expressed as a percentage:

$\text{Efficiency} = \frac{\text{Useful energy output}}{\text{Total energy input}} \times 100$

Electrical power plays a crucial role in various fields such as heating, lighting, and mechanical work. Understanding its relationship with voltage, current, and resistance helps in efficient use of electrical energy in everyday life.