Know the difference between direct current (d.c.) and alternating current (a.c.)

4.2.2 Electric Current

Objective

Know the difference between direct current (d.c.) and alternating current (a.c.).

Key Definitions

• Direct Current (d.c.): Electric charge flows in one constant direction.
• Alternating Current (a.c.): Electric charge changes direction periodically.

Characteristics of d.c. and a.c.

Mathematical Description of a Sinusoidal a.c.

The instantaneous current \$i(t)\$ in a simple sinusoidal alternating circuit can be expressed as

\$i(t)=I_{\text{max}}\sin(2\pi ft)\$

where:

• \$I_{\text{max}}\$ – maximum (peak) current
• \$f\$ – frequency in hertz (Hz)
• \$t\$ – time in seconds

Why RMS \cdot alues Are Used for a.c.

RMS (Root‑Mean‑Square) values allow an alternating current to be compared directly with a direct current in terms of heating effect. For a sinusoidal waveform:

\$I{\text{rms}} = \frac{I{\text{max}}}{\sqrt{2}}\$

Similarly, the RMS voltage is \$V{\text{rms}} = \dfrac{V{\text{max}}}{\sqrt{2}}\$.

Practical Implications

1. Transmission: a.c. can be stepped up or down with transformers, reducing losses over long distances.
2. Safety: a.c. at household frequencies can cause muscle tetany, whereas d.c. tends to cause a single shock.
3. Device design: electronic circuits often require d.c.; therefore, a.c. mains supply is rectified to d.c. using diodes.