AP Physics C E and M 11.3: Resistance of an Object

Describe resistance from an object’s material properties, length, cross-sectional area, and resistivity in a circuit model.

[Maximum number: 8]

In Experiment 1, students are asked to use a graph to determine the resistivity $\rho_{1}$ of a circuit

element that is connected to a variable power supply, as shown in Figure 1. The circuit element

is cylindrical and has uniform resistivity. The students have access to a voltmeter, an ammeter,

and a ruler.

Figure 1

(a)

Describe a procedure for collecting data that would allow the students to use a graph to

determine $\rho_{1}$ , including any steps necessary to reduce experimental uncertainty.

[ 2 ]

(b)

In Experiment 2, the students are asked to use a graph to determine the resistivity $\rho_{2}$ of solid,

cylindrical resistors made of the same material but of different lengths L. The cross-sectional

area of each resistor is $5.0 \times 10^{-6} \mathrm{~m}^{2}$ . The students directly measure the resistance R between the

ends of each resistor. Table 1 provides L and R for each resistor.

Table 1

[ 4 ]

(i)

Indicate two quantities, either measured quantities from Table 1 or additional calculated

quantities, that could be graphed to produce a straight line that could be used to

determine $\rho_{2}$ .

Vertical axis:

Horizontal axis:

[ 1 ]

For indicating appropriate quantities that could be plotted on the graph to determine $\rho_{2}$ , for example R as a function of L. — Point C1

Scoring Note: This point may be earned if the vertical and horizontal variables are reversed, or for other equivalent graphs.

(ii)

On the grid provided, create a graph of the quantities indicated in part C (i).

- Use Table 2 to record the measured or calculated quantities that you will plot.

- Clearly label the axes, including units as appropriate.

- Plot the points you recorded in Table 2.

Figure for Question (ii) — AP Physics C: Electricity & Magnetism

[ 2 ]

(iii)

Draw a best-fit line for the data graphed in part C (ii).

[ 1 ]

(c)

Using the best-fit line that you drew in part C (iii), calculate an experimental value for $\rho_{2}$ .

[ 2 ]

D For correctly relating the slope of the best-fit line to $\rho_{2}$

Point D1

$\text { (e.g., } \frac{\Delta R}{\Delta L}=\text { slope }=\frac{\rho_{2}}{A} \text { ) }$

For a value for $\rho_{2}$ that is between $3.5 \times 10^{-4} \Omega \cdot \mathrm{~m}$ and $4.5 \times 10^{-4} \Omega \cdot \mathrm{~m}$

Point D2

Example Response

$\begin{aligned} & \text { slope }=\frac{\Delta R}{\Delta L} \\ & \frac{\Delta R}{\Delta L}=\frac{4.0 \Omega-2.0 \Omega}{0.050 \mathrm{~m}-0.024 \mathrm{~m}} \\ & \frac{\Delta R}{\Delta L}=77 \frac{\Omega}{\mathrm{~m}} \\ & R=\frac{\rho L}{A} \\ & R=\left(\frac{\rho_{2}}{A}\right) L \\ & \text { slope }=\frac{\rho_{2}}{A} \\ & \rho_{2}=A(\mathrm{slope}) \\ & \rho_{2}=\left(5.0 \times 10^{-6} \mathrm{~m}^{2}\right)\left(77 \frac{\Omega}{\mathrm{~m}}\right) \\ & \rho_{2} \approx 3.9 \times 10^{-4} \Omega \cdot \mathrm{~m} \end{aligned}$

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11.3.A—Describe the resistance of an object using physical properties of that object question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (c)