Question

Alternating Current (ac) Circuits The current I, in amperes, flowing through an ac (alternating current) circuit at time t in seconds, is

$I\left(t\right)=120\sin \left(30\pi t\right)t\ge 0$

What is the period? What is the amplitude? Graph this function over two periods.

Short answer

Period and amplitude of the given function $T=\frac{1}{15}andA=120$respectively

Graph of the given function

Step-by-step solution

Step 1.Given information

The given function$I\left(t\right)=120\sin \left(30\mathrm{\pi t}\right)$

Step 2.Find the period and amplitude of the given function

For the given current function $I\left(t\right)=120\sin \left(30\mathrm{\pi t}\right)$, we can find the amplitude and period by comparing it with $y=A\sin \left(\omega t\right)$So, $A=120$and$\omega =120\pi$ and hence we can find the period

$$\begin{gathered} T=\frac{2\mathrm{\pi }}{\omega } \\ =\frac{2\mathrm{\pi }}{30\pi } \\ =\frac{1}{15} \end{gathered}$$

Thereforerole="math" localid="1646391797078" $T=\frac{1}{15}andA=120$

Step 3.Plot the graph by using period and amplitude

The required graph of the given function