Alternating Current

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Equation: I = I0 sin ωt. The current changes periodically in magnitude and direction. Peak value I0 is the maximum value reached by the current in a cycle. Units: I in ampere, ω in rad s^-1, t in s.

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Given: I = 6 sin(314 t) A Step 1: Compare with I = I0 sin ωt. So, I0 = 6 A and ω = 314 rad s^-1. Step 2: Period T = 2π/ω = 2π/314 s ≈ 0.02 s. Step 3: Frequency f = 1/T = 50 Hz. Answer: Peak current = …

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Formula: V0 = NBAω. Here, N = number of turns, B = magnetic field, A = area of coil, ω = angular velocity. The induced emf becomes maximum when the rotating coil cuts magnetic flux most effectively.

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Given: Vrms = 220 V Formula: Vrms = V0/√2 Step 1: V0 = √2 × Vrms Step 2: V0 = 1.414 × 220 V = 311 V Answer: Peak voltage = 311 V.

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AC changes direction very rapidly, so the torque on the galvanometer needle also changes direction. Because of inertia, the needle cannot follow these rapid reversals and remains nearly at rest. This …

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Mean value over one complete cycle = 0. Mean value over one half-cycle: Im = (2/π)I0 = 0.637 I0. The full-cycle mean is zero because positive and negative halves cancel each other.

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Given: I0 = 10 A Step 1: Irms = I0/√2 = 10/1.414 A = 7.07 A Step 2: Im = 0.637 I0 = 0.637 × 10 A = 6.37 A Answer: rms value = 7.07 A, half-cycle mean value = 6.37 A.

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The mean value over a full cycle is zero, so it cannot represent the heating effect of AC. The rms value is based on the same heating effect as DC and gives the effective value of AC in a circuit.