An alternating current is given by the equation $I=10\sin (314t)$. What is the frequency of this current in Hertz?

Solution

1. The standard form of an alternating current equation is $I=I_0\sin (\omega t)$, where $\omega$ is the angular frequency.
2. Comparing $I=10\sin (314t)$ to the standard form, we identify $\omega =314\text{ rad/s}$.
3. Using the relationship $\omega =2\pi f$, we solve for frequency: $$\begin{array}{rl}f& =\frac{\omega }{2\pi }\\ & =\frac{314}{2\times 3.14}\end{array}$$.
4. Calculating the value gives $$\begin{array}{rl}f& =\frac{314}{6.28}\\ & =50\text{ Hz}\end{array}$$.
5. Hence the answer is (A).