Explain the concepts of electrical energy and power, including their commercial units and the principles of power transmission.

Here are notes based on the objectives for Electrical Energy and Power:

• i) Concepts of electrical energy and power & applying expressions to solve problems:

  • Electrical Energy ($E$) is the work done by electric current. It is measured in Joules (J). $$E = VIt = I^2Rt = \frac{V^2}{R}t$$
  • Electrical Power ($P$) is the rate at which electrical energy is consumed or produced. It is measured in Watts (W). $$P = VI = I^2R = \frac{V^2}{R}$$

• ii) Commercial unit of electric energy and power: The commercial unit of electrical energy is the kilowatt-hour (kWh).

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

  Power is typically measured in Watts (W) or kilowatts (kW) for commercial purposes.

• iii) Electric power transmission & analyzing how power is transmitted:

  • Electricity is generated at power stations and transmitted over long distances at very high voltages (e.g., hundreds of kilovolts) to minimize power loss.
  • Step-up transformers increase the voltage at the power station.
  • Power loss in transmission cables is given by $P_{loss} = I^2R_{cable}$. By increasing voltage ($V$), the current ($I$) for a given power ($P=VI$) is reduced, significantly decreasing $I^2R$ losses.
  • Step-down transformers reduce the voltage for distribution to homes and industries for safety and usability.

• iv) Heating effects of electric current & its uses:

  • The heating effect of electric current (Joule heating) occurs when current flows through a resistor, converting electrical energy into heat energy. The heat produced is $H = I^2Rt$.
  • Uses: Electric heaters, toasters, kettles, electric irons, incandescent light bulbs, and fuses.

• v) Electrical wiring of houses & advantages of parallel arrangement over series:

  • Houses are wired in a parallel arrangement.
  • Advantages of parallel wiring:
    • Each appliance receives the full supply voltage.
    • Appliances can be switched on and off independently.
    • If one appliance fails, others continue to operate.
  • Disadvantages of series wiring: Appliances would not receive full voltage, could not be operated independently, and the failure of one would break the entire circuit.

• vi) Use of fuses & determining the fuse rating:

  • A fuse is a safety device that protects electrical circuits and appliances from overcurrent. It contains a thin wire that melts and breaks the circuit if the current exceeds a safe limit.
  • The fuse rating is the maximum current a fuse can carry continuously without melting.
  • To determine the fuse rating for an appliance, calculate its normal operating current using the formula $I = \frac{P}{V}$, where $P$ is the power of the appliance and $V$ is the supply voltage. The fuse rating should be slightly higher than this calculated current.
  • For example, a 2400 W appliance on a 240 V supply draws $I = \frac{2400 \text{ W}}{240 \text{ V}} = 10 \text{ A}$. A 13 A fuse would be appropriate.