Chapter 18, Problem 66GP

(a)

To determine

The frequency.

Answer to Problem 66GP

  $33.4Hz$

Explanation of Solution

Given:

Angular frequency, $\varpi =210rd/s$

The value of $\pi =3.14$

Current, $I=1.80A\left(\sin 210t\right)$

Formula used:

Formula to calculate the frequency:

  $f=\frac{\varpi }{2\pi }$

Where,

  $f$ is frequency

  $\varpi$ is angular frequency

  $\pi$ is constant.

Calculation:

By using the formula of frequency: $f=\frac{\varpi }{2\pi }$

Substitute all the given values:

  $f=\frac{\varpi }{2\pi }=\frac{210rd/s}{2\pi }=33.4Hz$

Conclusion: The required frequency is $33.4Hz$ .

(b)

To determine

The rms value of the current.

Answer to Problem 66GP

  $1.27A$

Explanation of Solution

Given:

Current, $I=1.80A\left(\sin 210t\right)$

Formula used:

Formula to calculate the rms value of the current:

  $I_{rms}=\frac{I_{\max }}{\sqrt{2}}$

Where,

  $I_{rms}$ is root mean square current

  $I_{\max }$ is the maximum current

Calculation:

By substituting all the given values in the expression: $I_{rms}=\frac{I_{\max }}{\sqrt{2}}$

  $I_{rms}=\frac{1.80A}{\sqrt{2}}=1.27A$

Conclusion: The rms value of the current is $1.27A$ .

(c)

To determine

The equation that describes the voltage as a function of time.

Answer to Problem 66GP

  $\left(75.6\sin 210t\right)V$

Explanation of Solution

Given:

Current, $I=1.80A\left(\sin 210t\right)$

Resistance, $R=42.0\Omega$

Formula used:

Expression to calculate voltage:

  $V=I\times R$

Where,

  $I$ is the current.

  $V$ is the voltage.

  $R$ is the resistance.

Calculation:

By substituting all the given values in the expression: $V=I\times R$

  $\begin{array}{c}V=\left(\text{1}\text{.80}\text{A}\right)\left(\text{sin}\text{210}\text{t}\right)\left(\text{42}\text{.0}\text{Ω}\right)\\ \text{=}\left(\text{75}\text{.6}\text{sin}\text{210}\text{t}\right)\text{V}\end{array}$

Conclusion: The required equation of voltage is $\left(75.6\sin 210t\right)V$ .