An alternating current is represented by the equation, i=100 √2 sin (100 π t) ampere. The RMS value of current and the frequency of the given alternating current are

Solution

Physics sir · 3 steps

Read the peak off the front of the sine and ω off the inside; then divide by √2 and by 2π.

1. Match the form. Compare with i = i₀ sin(ω t). The number in front is the peak current, i₀ = 100√2 A, and the number multiplying t is ω = 100π rad s⁻¹.
2. RMS current. For a sinusoidal current, iᵣₘₛ = i₀/√2 = 100√2/√2 = 100 A.

   f = ω/2π = 100π/2π = 50 Hz

3. So. The RMS current is 100 A and the frequency is 50 Hz, which is option (d).

The idea to keep. In i = i₀ sin(ω t), the coefficient is the peak value and the number beside t is ω, not f. RMS is peak over √2; frequency is ω over 2π.

Answer from the NTA final answer key. Solution by PrepWiser.