# Electric Power & Energy

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## Electricity

Electricity plays a pivotal role in powering our modern world, seamlessly transforming into various forms of energy through the operation of diverse electrical devices. However, this powerful resource comes with its risks. Unsafe practices in handling electricity can lead to devastating consequences, including electrical fires and shocks, potentially causing serious injuries or even fatalities. To mitigate these dangers, incorporating safety mechanisms such as fuses, circuit breakers, switches, and earthing (grounding) wires is essential. These features are designed to interrupt power in abnormal conditions, preventing electrical fires and reducing the risk of electric shocks, thereby safeguarding users from harm.

## The Heating Effect Of Electricity

One of the most familiar phenomena associated with electricity is its ability to produce heat. This is known as the heating effect of electric current, where electrical energy is converted into thermal energy as current flows through a resistor. This principle underpins the operation of many household appliances that generate heat, such as electric kettles, ovens, heaters, irons, hair dryers, toasters, and electric cookers. The core of these appliances contains a heating element, typically made from materials with high resistance like nichrome wire. The extent of the heating effect can be controlled by adjusting the current flowing through this element, allowing for precise temperature management.

Beyond heating, electricity’s versatility is showcased in its magnetic and chemical effects, as seen in applications like electromagnets and electrolysis, respectively. This highlights electricity’s broad utility across various fields.

## Power Of An Electrical Appliance

The rate of the heating effect is quantified in terms of power, measured in kilowatts (kW), while the total energy conversion is gauged in kilowatt-hours (kWh). The power (P) of an electrical appliance can be calculated through the equations:

\begin{aligned} P &= I^{2}R \\ &= \frac{V^{2}}{R} \\ &= VI \end{aligned}

where,
$V$ = voltage applied across appliance
$I$ = current flowing through appliance
$R$ = total resistance of appliance

SI unit for power is the kilowatt (kW), where 1 kW equals 1000 watts (W) or 1000 joules per second ($\text{J s}^{-1}$).

## Energy Conversion In Electrical Appliance

The energy converted by an electrical appliance over a period of time is given by the formula:

\begin{aligned} E &= P \times t \\ &= I^{2}R \: \times \: t \\ &= \frac{V^{2}}{R} \: \times \: t \\ &= VI \: \times \: t \end{aligned}

where,
$V$ = voltage applied across appliance
$I$ = current flowing through appliance
$R$ = total resistance of appliance
$t$ = total time taken

SI unit for energy conversion is the kilowatt-hour (kWh), where:

$$1 \text{kWh} = (1000 \text{W}) \times (60 \times 60 \text{s}) = 3 600 000 \text{J} = 3600 \text{kJ} = 3.6 \text{MJ}$$

Appliances with higher power ratings consume more electrical energy in a given time frame.

## Efficiency & Cost Implications

Electrical appliances are indispensable in our daily lives, yet it’s essential to understand that they do not operate at perfect efficiency. In practical terms, efficiency refers to the proportion of input energy that is successfully converted into the appliance’s intended output (for example, heat in a heater or light in a lamp). The remaining energy is not lost but is instead transformed into other, often less desirable forms of energy such as sound or light (in the case of non-light producing appliances), and heat in devices not intended to produce it. This inherent inefficiency affects both the operational cost and the environmental footprint of using electrical appliances.

The formula to calculate the efficiency ($\eta$) of an electrical appliance is given by:

$$\eta = \left( \frac{\text{Useful energy output}}{\text{Total energy input}} \right) \times 100\%$$

Understanding efficiency is crucial for several reasons. Firstly, it directly impacts the cost of operating the appliance. Higher efficiency means more of the electrical energy you’re paying for is converted into the work you want (like cooling your room or cooking your food), which translates to lower electricity bills over time. Secondly, efficiency has environmental implications; more efficient appliances use less power for the same output, reducing the demand on power plants and thereby potentially lowering greenhouse gas emissions.

The consumption of electrical energy in domestic settings is meticulously quantified using meters that measure in kilowatt-hours (kWh). The cost of energy consumption is straightforwardly calculated by multiplying the number of kilowatt-hours consumed by the rate charged per kilowatt-hour. This rate can vary significantly depending on geographical location, time of use, and the energy provider’s pricing scheme.

Monthly monitoring of energy usage, facilitated by reading the electricity meter, allows households to track their electrical energy consumption accurately. The difference in meter readings from the end of one month to the end of the next provides a clear picture of the current month’s consumption. This transparent system not only aids in understanding and managing energy use but also encourages the adoption of more energy-efficient appliances and habits, leading to cost savings and environmental benefits.

In summary, while electrical appliances provide numerous conveniences and comforts, their efficiency plays a pivotal role in determining their operational cost and environmental impact. By choosing high-efficiency models and being mindful of our energy consumption habits, we can enjoy the benefits of these appliances while also contributing to a more sustainable and cost-effective use of electrical energy.

## Worked Examples

### Example 1: Power Calculation

An electric kettle with a resistance of 30 ohms is connected to a 220-volt power supply. What is the power consumption of the kettle?

Power can be calculated using $P = \frac{V^2}{R}$.

Given $V = 220$ volts and $R = 30$ ohms,

\begin{aligned} P &= \frac{220^2}{30} \\ &= \frac{48400}{30} \\ &= 1613.33 \, \text{W} \\ &= 1.6 \text{ kW} \end{aligned}

The kettle consumes 1.6 kilowatts of power.

### Example 2: Energy Conversion

If the electric kettle from Example 1 is used for 2 hours, how much energy (in kWh) does it consume?

Using $E = P \times t$,

Given $P = 1.6$ kW (from Example 3) and $t = 2$ hours,

$$E = 1.6 \, \text{kW} \times 2 \, \text{hours} = 3.2 \, \text{kWh}$$

The kettle consumes 3.2 kilowatt-hours of energy.

### Example 3: Efficiency and Cost

Assuming the cost of electricity is $0.15 per kWh, calculate the cost of operating the electric kettle from Example 1 for 2 hours. Click here to show/hide answer Given the energy consumption is 3.2 kWh (from Example 4) and the cost is$0.15 per kWh,

$$\text{Cost} = 3.2 \, \text{kWh} \times \0.15/\text{kWh} = \0.48$$

It costs \$0.48 to operate the kettle for 2 hours.

### Example 4: Understanding Appliance Efficiency

An electric toaster has a power rating of 1 kW and operates for 0.5 hours, consuming 0.5 kWh of energy. If the toaster converts 90% of the electrical energy to thermal energy, how much energy is wasted in forms other than heat?

Total energy consumed is 0.5 kWh. 90% of this energy is used as thermal energy, so:

$$\text{Useful energy} = 0.5 \, \text{kWh} \times 0.9 = 0.45 \, \text{kWh}$$

\begin{aligned} \text{Energy wasted} &= \text{Total energy} – \text{Useful energy} \\ &= 0.5 \, \text{kWh} – 0.45 \, \text{kWh} \\ &= 0.05 \, \text{kWh} \end{aligned}

Thus, 0.05 kilowatt-hours of energy is wasted in forms other than heat.

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