The peak value of an alternating voltage is 220 V and its frequency is 50 Hz. What is the minimum time taken by the voltage to reach half of its peak value, starting from zero?

Step-by-step solution

The equation for an alternating voltage starting from zero is given by V = V₀ ( t) . We are given that the voltage reaches half of its peak value, so V = V₀ 2 . Substituting this into the equation, we get: V₀ 2 = V₀ ( t) ( t) = 1 2 For the minimum time, the phase angle should be the smallest positive value, which is 6 . t = 6 Substituting = 2 f , we get: 2 f t = 6 t = 1 12f Given the frequency f = 50 Hz, the minimum time is: t = 1 12 50 = 1 600 s Answer: 1 600 s