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Find the time required for a 50 Hz alternating current to change its value form zero to the rms value.

Find the time required for a 50 Hz alternating current to change its value form zero to the rms value.

Grade:upto college level

3 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Sol. f = 50 Hz I = I base 0 Sin Wt Peak value I = I base 0/√2 I base 0/√2 = I base 0 Sin Wt ⇒ I base 0/√2 Sin Wt = Sin π/4 ⇒ π/4 = Wt. or, t = π/400 = π/4 * 2πf = 1/8f = 1/8 * 50 = 0.0025 s = 2.5 ms
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty
Kushagra Madhukar
askIITians Faculty 629 Points
one year ago
Dear student,
Please find the solution to your problem below.

Let the equation of alternating current be
V(t) = v sin (2πft) = v sin (2π50t) = v sin (100πt)
Now, vrms = v/2
Hence, v sin (100πt) = v/2
or, sin (100πt) = 1/root2
or 100πt = π/4
or, t = 1/400 s = 2.5 x 10-3 s = 2.5 ms

Hope it helps.
Thanks and regards,
Kushagra

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