The instantaneous current in a circuit is given by i = 4sin(ωt + π/4). The RMS value of the current is

JAMB Physics 2024 199 views
Source: JAMB · 2024

The instantaneous current in a circuit is given by i = 4sin(ωt + π/4). The RMS value of the current is

  1. 1.92 A
  2. 5.66 A
  3. 4.22 A
  4. 2.83 A ✓
Explanation

For i = I₀ sin(ωt + φ), the peak current is I₀ = 4 A. The phase angle π/4 does not change the RMS value.

I(rms) = I₀ ÷ √2 = 4 ÷ 1.414 ≈ 2.83 A.

5.66 A is I₀ × √2, which is a common mistake.

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