Question

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

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

Answer 1

Answer: (C)

We are given that, $\varepsilon_{ rms }=220\, V , v=50\, Hz$
As, $\varepsilon_{ rms }=\frac{\varepsilon_{0}}{\sqrt{2}}, \varepsilon_{0}=\varepsilon_{ rms } \sqrt{2}$
$(220\, V )(1.414)=311.1\, V$
Further, $\omega=2 \pi v=2 \pi \times 50=100 \pi$ rads $^{-1}$
Thus, the equation for the instantaneous voltage is given as $\varepsilon=\varepsilon_{0} \sin (1) t=311.1\, V \sin (100 \pi) t$