Alternating current circuits

1. Understanding Alternating Current (AC)

• Alternating current $(AC)$ changes direction periodically.

• Frequency $(f)$: The number of complete cycles per second (Hertz, Hz).

  • In South Africa, AC electricity has a frequency of 50 Hz.

• Period $(T)$: The time taken for one complete cycle. $T = \frac{1}{f}$

  • For $50$ $Hz,$ the period is $0.02 s$.

2. Voltage and Current in an AC Circuit

• Voltage $(V)$ and current $(I)$ vary in cycles.
• Key Terms:
  • Vmax (Maximum Voltage): Peak voltage value.
  • Irms (Root Mean Square Current): Effective current value in AC circuits.
  • Vrms (Root Mean Square Voltage): Equivalent DC voltage that produces the same power as AC.

Formulas:

$V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}, \quad I_{\text{rms}} = \frac{I_{\text{max}}}{\sqrt{2}}$

3. Electric Power in an AC Circuit

• Power $(P)$ is the rate at which energy is transferred.
• Key Power Equations: $P = V_{\text{rms}} I_{\text{rms}}$

$P = I^2 R$

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

• In DC circuits, power is calculated using $P = VI.$

4. Advantages of Alternating Current

• AC voltage can be changed using transformers.
• Efficient for power transmission:
  • Step-up transformers increase voltage, decreasing current.
  • Step-down transformers decrease voltage for household use (220 V in South Africa).
• Reduced energy loss:
  • Lower current = Less heat loss in transmission lines.
  • High-voltage transmission improves efficiency.

5. Key Takeaways

• AC voltage varies cyclically, unlike steady DC voltage.
• Root Mean Square (RMS) values help compare AC to DC.
• Transformers work only with AC, making it ideal for electricity distribution.
• Power calculations in AC circuits use RMS values.