An alternating current is given by the equation $I=10\sin (100\pi t)$. What is the frequency of this current in Hertz?

Solution

1. The standard form of an AC current is $I=I_0\sin (\omega t)$.
2. Comparing this with $I=10\sin (100\pi t)$, we get $\omega =100\pi$.
3. Since $\omega =2\pi f$, we have $2\pi f=100\pi$.
4. Solving for $f$, we get $f=50\text{ Hz}$.
5. Hence the answer is (A).