If a sinusoidal wave has frequency of 50 Hz with 30 A r.m.s. current which of the following equation represents this wave?

42.42 sin 314 t
60 sin 25 t
30 sin 50 t
84.84 sin 25 t

The correct answer is $\boxed{\text{C) }30 \sin 50 t}$.

The equation for a sinusoidal wave with frequency $f$ and amplitude $A$ is $y = A \sin(2 \pi f t)$. In this case, the frequency is $f = 50 \text{ Hz}$ and the amplitude is $A = 30 \text{ A}$. Substituting these values into the equation, we get $y = 30 \sin(2 \pi \times 50 t)$. This can be simplified to $y = 30 \sin 1000 t$.

The other options are incorrect because they do not have the correct frequency or amplitude. Option A has a frequency of $314 \text{ Hz}$, which is not the same as the given frequency of $50 \text{ Hz}$. Option B has an amplitude of $60 \text{ A}$, which is not the same as the given amplitude of $30 \text{ A}$. Option D has a frequency of $25 \text{ Hz}$, which is not the same as the given frequency of $50 \text{ Hz}$ and an amplitude of $84.84 \text{ A}$, which is not the same as the given amplitude of $30 \text{ A}$.