Q. 88 - Precalculus Enhanced with Graphing Utilities

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. 

Step-by-Step Solution

Answer

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

Graph of the given function

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

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

Therefore  $T=\frac{1}{15} and A=120$

Step 3.Plot the graph by using period and amplitude

The required graph of the given function