Chapter 8, Problem 1P

Given $i\left(t\right)=5\cos \left(400t-120°\right)\text{A}$, determine the period of the current and the frequency in Hertz.

To determine

The Period of the current and the Frequency in Hertz.

Answer to Problem 1P

Frequency $\left(\text{f}\right)$ = 63.66 Hz

Time period $\left(\text{T}\right)$ =15.7 m/sec

Explanation of Solution

Given Information:

$\text{i(t)=5 cos (400t-120°)}$

In general,  $\omega$ is the angular speed - the rate change of angle (as in a circular motion). Frequency is $1/T$ or the number of periodic oscillations or revolutions during a given time period.

It is known that

$\omega =\frac{2\pi }{T}$

In the given equation of current

$\omega =400\text{rad/sec}$

Hence,

$\begin{array}{l}400=\frac{2\pi }{T}\\ T=\frac{2\pi }{400}\\ T=15.70\times {10}^{-3}\\ T=15.70\text{msec}\end{array}$

Although,

$\begin{array}{l}f=\frac{1}{T}\\ \text{plugging}\text{value}\\ f=\frac{1}{15.70\times {10}^{-3}}\\ f=63.69\text{Hz}\end{array}$