The current flowing through an ac circuit is given by
I = 5 sin(120πt)A
How long will the current take to reach the peak value starting from zero?

Solution

Physics sir · 3 steps

Zero to peak is a quarter of a cycle, so just find when the sine's angle reaches π/2.

1. Read off omega. Compare I = 5 sin(120π t) with I = I₀ sin(ω t). So ω = 120π rad s⁻¹, which means f = 60 Hz and T = 1/60 s.
2. Peak condition. The current starts at zero at t = 0 and first reaches its peak 5 A when sin(ω t) = 1, that is, when ω t = π/2.

   120π t = π/2 ⇒ t = 1/240 s

3. So. This is T/4 = 1/4 × 1/60 = 1/240 s, which is option (d).

The idea to keep. In a sine wave, zero to peak is always T/4. Get T from ω = 2π f, then divide by 4.

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