average

average

1. What Average Value Is

Average (mean) value $V_{avg}, I_{avg}$ over a full period $T$:

For pure sine over full cycle, $V_{avg}=0$ (positive half cancels negative). So we consider half-wave average (or full-wave rectified average):

• Sine half-wave ($0$ to $π$):

• Sine full-wave rectified ($|v|$): same $2V_m/π$ (since both halves positive).
• Full cycle sine $V_{avg}=0$.

2. Why Average Matters

• Moving-coil meter (DC) measures average (for rectified AC via bridge, it reads $2V_m/π$ but scaled to RMS for sine).
• Battery charging with half-wave: average determines charge.
• Not for power — power uses RMS, not average (heating).

3. Worked Values (memorize for sine)

Half-wave sine V_m=10V ⇒ V_avg=6.37V (half-wave), full-wave also 6.37V for |v|; full-cycle without rectification 0.

Square wave 5V 50% duty V_avg=0 for full cycle (±5), but rectified avg=5V.

If average is zero, use RMS for power.

Need to convert: For sine, V_avg (half) =0.637V_m, V_rms=0.707V_m ⇒ Form factor = V_rms/V_avg≈1.11 (next topic)

4. Exam Points

• Define $V_{avg}=1/T∫v dt$ and $V_{avg}=0$ for full sine, $2V_m/π$ for half/full rectified — 5 marks, very frequent (almost certain to ask).
• Compute for $V_m=10V$ ⇒ $6.37V$ — 5 marks, frequent.
• Mention moving-coil reads average — 3 marks.