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

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
7 years ago
Hello
$\\v(t)=vsin(2\pi 50t) \\v_{rms}={ v \over \sqrt2} \\=>so v(t)=0 at t=0 \\=>v(t)={v \over \sqrt2} \\=>2\pi 50t={\pi \over 4} \\=>t={1 \over 100}$
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
one year ago
Dear student,

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