Chapter 6, Problem 46R

To determine

To calculate: the resistance of each circuit.

To graph the current versus the resistance of each circuit and describe the shape of the line obtained.

Answer to Problem 46R

The resistance of the circuits are

  $\begin{array}{l}{R}_A=2.6\Omega \\ R_B=10\Omega \\ R_C=30\Omega \\ R_D=3.33\Omega \end{array}$

The current versus resistance of each circuit:

  

The graph shows that resistance decreases with increase in current.

Explanation of Solution

Given data:

The table:

  

Voltage difference across each circuit, $V=6\text{ V}$

Formula used:

Ohm’s law equation:

  $I=\frac{V}{R}$

Where $I$ is the current in a circuit in amperes, $V$ is the voltage difference across the circuit in volts and $R$ is the resistance of the circuit in ohms.

Calculation:

As per the problem,

From the given table, consider

• Circuit A

  $\begin{array}{l}V=6\text{ V}\\ I_A=2.3\text{ A}\end{array}$

Substitute the values voltage difference and current in the rearranged ohm’s law equation to get resistance:

  $\begin{array}{l}{I}_A=\frac{V}{R_A}\\ R_A=\frac{V}{I_A}\\ R_A=\frac{6\text{ V}}{2.3\text{ A}}=2.6\Omega \end{array}$

• Circuit B

  $\begin{array}{l}V=6\text{ V}\\ I_B=0.6\text{ A}\end{array}$

Substitute the values voltage difference and current in the rearranged ohm’s law equation to get resistance:

  $\begin{array}{l}{R}_B=\frac{V}{I_B}\\ R_B=\frac{6\text{ V}}{0.6\text{ A}}=10\Omega \end{array}$

• Circuit C

  $\begin{array}{l}V=6\text{ V}\\ I_C=0.2\text{ A}\end{array}$

Substitute the values voltage difference and current in the rearranged ohm’s law equation to get resistance:

  $\begin{array}{l}{R}_C=\frac{V}{I_C}\\ R_C=\frac{6\text{ V}}{0.2\text{ A}}=30\Omega \end{array}$

• Circuit D

  $\begin{array}{l}V=6\text{ V}\\ I_D=1.8\text{ A}\end{array}$

Substitute the values voltage difference and current in the rearranged ohm’s law equation to get resistance:

  $\begin{array}{l}{R}_D=\frac{V}{I_D}\\ R_D=\frac{6\text{ V}}{1.8\text{ A}}=3.33\Omega \end{array}$

Tabulate the resistance of each corresponding to the current in the circuit:

  

Graph the current versus resistance of each circuit:

  

The graph shows that resistance decreases with increase in current.

Conclusion:The resistance of the circuits are

  $\begin{array}{l}{R}_A=2.6\Omega \\ R_B=10\Omega \\ R_C=30\Omega \\ R_D=3.33\Omega \end{array}$

The current versus resistance for each circuit graph shows that resistance decreases with increase in current.