Chapter 8.4, Problem 27PPS

a.

To determine

To graph:

The given function where $R_1$ is the independent variable and $I$ is the dependent variable

Explanation of Solution

Given information:

The current in amperes in electric circuit is $I=\frac{V}{R_1+R_2+R_3}$ , here $V$ is the voltage in volts and $R_1,R_2,R_3$ are the resistance in ohms

The voltage $\left(V\right)$ is 120 volts

The resistance $R_2$ is 25 ohms and $R_3$ is 75 ohms

Graph:

  

Interpretation:

The given values of voltage and resistance are put the given formula then the value for current is obtained. The obtained data is plotted and hence the graph is obtained.

b.

To determine

To give the equation for the vertical asymptote and the $R_1$ -intercepts and $I$ -intercepts of the graph

Answer to Problem 27PPS

The vertical asymptote is $R_1=-100$ and here is no $R_1$ -intercepts and $I$ -intercepts approaches to zero.

Explanation of Solution

Given information:

The current in amperes in electric circuit is $I=\frac{V}{R_1+R_2+R_3}$ , here $V$ is the voltage in volts and $R_1,R_2,R_3$ are the resistance in ohms

The voltage $\left(V\right)$ is 120 volts

The resistance $R_2$ is 25 ohms and $R_3$ is 75 ohms

The given function is,

  $I=\frac{V}{R_1+R_2+R_3}$ Or $I=\frac{120}{R_1+25+75}=\frac{120}{R_1+100}$

To find vertical asymptotes put the denominator equal to zero

So, $R_1+100=0$ or $R_1=-100$

Therefore, the vertical asymptote is $R_1=-100$

There is no $R_1$ -intercepts; the function asymptotically approaches $I=0$ . The $I$ -intercepts occurs when $R_1$ is zero or $I=\frac{120}{0+25+75}=1.2$ amperes

Therefore, the vertical asymptote is $R_1=-100$ and here is no $R_1$ -intercepts and $I$ -intercepts approaches to zero.

c.

To determine

To calculate:

The value of current $\left(I\right)$ in amperes

Answer to Problem 27PPS

The value of current $\left(I\right)$ is 0.5 amperes.

Explanation of Solution

Given information:

The current in amperes in electric circuit is $I=\frac{V}{R_1+R_2+R_3}$ , here $V$ is the voltage in volts and $R_1,R_2,R_3$ are the resistance in ohms

The voltage $\left(V\right)$ is 120 volts

The resistance $R_1$ is 140 ohms, $R_2$ is 25 ohms and $R_3$ is 75 ohms

Calculation:

The value of current can be calculated as,

  $\begin{array}{l}I=\frac{V}{R_1+R_2+R_3}\\ I=\frac{120}{140+25+75}\\ I=\frac{120}{240}\\ I=0.5\text{ amperes}\end{array}$

Therefore, the value of current $\left(I\right)$ is 0.5 amperes.

d.

To determine

To find out what values of domain and range are meaningful in the context of the problem

Answer to Problem 27PPS

The value of domain should be $R_1>0$ and range should be $I>0$ then the context of the problem will be meaningful

Explanation of Solution

Given information:

The current in amperes in electric circuit is $I=\frac{V}{R_1+R_2+R_3}$ , here $V$ is the voltage in volts and $R_1,R_2,R_3$ are the resistance in ohms

In the problem context, current is non-negative value. Therefore, the domain should be restricted to the values greater than zero that is $R_1>0$ and the range should be $I>0$ . For these values of domain and range the context of the problem will be meaningful.