Question

The electric mains in the house is marked $220V,50Hz$. Write down the equation for instantaneous voltage.

• A. $3.1V\sin (100\pi )t$
• B. $31.1V\cos (100\pi )t$
• C. $311.1V\sin (100\pi )t$
• D. $311.1V\cos (100\pi )t$

Answer 1

Answer: (C)

We are given that, ${\epsilon }_{rms}=220V,v=50Hz$
As, ${\epsilon }_{rms}=\frac{{\epsilon }_0}{\sqrt{2}},{\epsilon }_0={\epsilon }_{rms}\sqrt{2}$
$(220V)(1.414)=311.1V$
Further, $\omega =2\pi v=2\pi \times 50=100\pi$ rads ${}^{-1}$
Thus, the equation for the instantaneous voltage is given as $\epsilon ={\epsilon }_0\sin (1)t=311.1V\sin (100\pi )t$