Q. 87 - 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

$I\left(t\right)=220\sin \left(60\omega t\right) t\ge 0$

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

Step-by-Step Solution

Answer

Period of the given function$220$

Amplitude of the given function $\frac{1}{30}$

Graph of the given function

Step 1.Given information

The amplitude and period, T of the functions $y=A\sin \left(\omega t\right)$ is given by,

Amplitude$=\left|A\right|$  and $T=\frac{2t}{\omega }$, when $\omega >0$
Compare $I\left(t\right)=220\sin \left(60\pi t\right)$ to the standard form $y=A\sin \left(\omega t\right)$, we get $A=220$ and $\omega =60\pi$

so,

$$\begin{gathered} T=\frac{2\pi }{60\pi } \\ =\frac{1}{30} \end{gathered}$$ .
Therefore, the period and the amplitude of the function $I\left(t\right)=220\sin \left(60\pi t\right)$ is $220$ and $\frac{1}{30}$ respectively.

Step 2.Plot the graph using period and amplitude of the given function