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# The household supply of electricity is at 220 V (rms value) and 50 Hz. Find the peak voltage and the least possible time in which the voltage can change crom the rms value to zero.

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Sol. E baserms = 220 V Frequency = 50 Hz (a) E base rms = E base 0/√2 ⇒ E base 0 = E base rms √2 =√2 * 220 = 1.414 * 220 = 311.08 V = 311 V (b) Tiem taken for the current to reach the peak value = Time taken to reach the 0 value from r.m.s I = I base 0/√2 ⇒ I base 0/√2 = I base 0 Sin ωt ⇒ ωt = π/4 ⇒ t = π/4∗ = π/4 *2πf = π/8π50 = 1/400 = 2.5 ms
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 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