Question

The household supply of electricity is at $220Vrms$ value and $50Hz$. Calculate the peak voltage and minimum possible time in which the voltage can change from the rms value of zero.

Answer 1

From definition of rms value,

$I_{rms}=\frac{I_o}{\sqrt{2}}$

$I_o=220\sqrt{2}=311.12V$

Now, $I=I_o\sin \left(2\pi ft\right)$

At rms value,

$\frac{I_o}{\sqrt{2}}=I_o\sin (2\pi \times 50t)$

$100\pi t_1=3\pi /4$

$t_1=3/400s=7.5ms$

At zero value,

$0=I_o\sin \left(2\pi ft\right)$

$2\pi \times 50t_2=\pi$

$t_2=10ms$

Time for transition, $t=t_2-t_1=2.5ms$