Topic 1 · 17.1–17.2 · Free
Topic Notes · Easy summaries with diagrams
Chapter 5 — Chapter 5 — Alternating Current
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📘Easy summary
An alternating current (AC) changes its magnitude and direction periodically. Cycle: one complete set of positive and negative values of an alternating quantity. Time period T: the time taken to complete one cycle (seconds). Frequency f: number of cycles per second (1 Hz = 1 cycle per second); f = 1/T. AC is easy to transfer over long distances, even between two cities, with small energy loss; DC cannot be transferred over very long distances economically. Instantaneous value V = V₀ sin ωt = V₀ sin 2πft. Peak value: highest value reached in one cycle; peak-to-peak value: total distance from positive to negative peak (= 2V₀). Average value of a full-wave rectified sine wave: I_av = 2I₀/π ≈ 0.637 I₀. The rms (effective) value is the steady DC value that produces the same heating effect (power dissipation) in a resistor: I_rms = I₀/√2 ≈ 0.707 I₀, V_rms = V₀/√2.
⭐Key points
- f = 1/T; ω = 2πf.
- V_rms = V₀/√2 = 0.707 V₀.
- V_pp = 2V₀; I_av (full-wave) = 2I₀/π.
🔬Diagram
🌿Real-life example
I = 420 sin(100πt): I_rms = 420/√2 ≈ 297 A; ω = 100π ⇒ f = 50 Hz.
💡Exam tip
- Meters read rms values; '220 V mains' means V_rms = 220 V, V₀ ≈ 311 V.
✅Quick check
1. rms value of AC of peak 10 A:
2. Peak-to-peak value of a sine wave of amplitude V₀:
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