Question

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 from the rms value to zero

Answer 1

Here $E_{rms}$ = 220 V,

Frequency = 50 Hz

(a) $E_{rms}=\frac{E_0}{\sqrt{2}}$

$\Rightarrow E_0=E_{rms}\sqrt{2}$

= $\sqrt{2}\times 220\times$ 1.414

= 34.08 V = 311 V

(b) Time taken for the current to reach the peak value = Time taken to reach the 0 value ffrom r.m.s.

i= $\frac{i_0}{\sqrt{2}}$

$\frac{i_0}{\sqrt{2}}=i_{0}sin\omega t$

$\omega t=\frac{\pi }{4}$

t= $\frac{\pi }{4\omega }=\frac{\pi }{4\times 2\pi f}$

= $\frac{\pi }{8\pi 50}=\frac{1}{400}$

= 2.5 ms