Electrical Energy and Power

1. Concepts of Electrical Energy and Power

Electrical Energy (W) is the work done by an electric current in a circuit over a period of time. Its SI unit is the Joule (J).

Electrical Power (P) is the rate at which electrical energy is consumed or converted into other forms of energy. Its SI unit is the Watt (W), where 1W = 1 J/s.

Mathematical Expressions

• Energy: $W = VIt = I^2Rt = \frac{V^2t}{R}$
• Power: $P = VI = I^2R = \frac{V^2}{R}$

Where: V = Voltage (Volts), I = Current (Amperes), R = Resistance (Ohms), and t = Time (Seconds).

2. Commercial Unit of Electric Energy

Electric companies bill consumers based on the Kilowatt-hour (kWh) rather than Joules because the Joule is too small for practical commercial use.

• 1 kWh = $1000W \times 3600s = 3.6 \times 10^6$ Joules.
• Cost of Electricity = Power (in kW) $\times$ Time (in hours) $\times$ Unit Price.

3. Electric Power Transmission

Power is transmitted from power stations over long distances at High Voltage and Low Current. This is achieved using step-up transformers at the source.

Reason: Power loss in cables ($P_{loss} = I^2R$) depends on the square of the current. By increasing the voltage, the current is reduced, thereby minimizing energy loss as heat in the transmission lines.

4. Heating Effects of Electric Current

When current flows through a conductor with resistance, it generates heat. This is known as Joule's Law of Heating ($H = I^2Rt$).

• Applications: Electric irons, kettles, toasters, water heaters, and incandescent bulbs.
• The heating element is usually made of materials with high resistivity and high melting points, such as Nichrome.

5. Electrical Wiring of Houses

House wiring consists of three main wires:

• Live Wire (Brown/Red): Carries the high voltage potential.
• Neutral Wire (Blue/Black): Provides the return path for current (zero potential).
• Earth Wire (Green/Yellow): A safety wire connected to the ground to prevent electric shocks.

Parallel vs. Series Arrangement

Domestic appliances are connected in parallel because:

• Each appliance receives the full mains voltage (220-240V).
• Appliances can be switched on or off independently.
• If one appliance fails, the circuit remains closed for others.

6. Fuses and Safety

A Fuse is a safety device consisting of a thin wire with a low melting point. It is always connected to the Live wire.

• Function: It melts and breaks the circuit when the current exceeds its rating, protecting the appliance.
• Fuse Rating: The maximum current a fuse can carry. To determine the correct fuse, calculate the operating current ($I = P/V$) and choose a fuse slightly higher than that value.