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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
9 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
9 years ago
Hello
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty
Kushagra Madhukar
askIITians Faculty 628 Points
3 years 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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