Draw a graph of Voltage vs. Current for the given series data and calculate its slope.

Question

ScanSolve AI Tutor · Accepted Answer

Okay, let's draw the graphs and determine the slopes for both the series and parallel data.

Graph for Series Data

Prepare the graph axes for Series
Draw a horizontal axis (x-axis) for Current $I$ (in Amperes, A) and a vertical axis (y-axis) for Voltage $V$ (in Volts, V).
- For the x-axis (Current), choose a scale that covers $0.02 \text{ A}$ to $0.10 \text{ A}$ .
- For the y-axis (Voltage), choose a scale that covers $0.40 \text{ V}$ to $2.00 \text{ V}$ .
Plot the data points for Series
Plot the following points on your graph paper:
- $(0.02 \text{ A}, 0.40 \text{ V})$
- $(0.04 \text{ A}, 0.80 \text{ V})$
- $(0.05 \text{ A}, 1.00 \text{ V})$
- $(0.08 \text{ A}, 1.60 \text{ V})$
- $(0.10 \text{ A}, 2.00 \text{ V})$
Draw the best-fit line for Series
Draw a straight line that passes through all the plotted points.
Determine the slope for Series
To calculate the slope, choose two distinct points on the best-fit line. We will use the first and last data points.
Point 1: $(I_1, V_1) = (0.02 \text{ A}, 0.40 \text{ V})$
Point 2: $(I_2, V_2) = (0.10 \text{ A}, 2.00 \text{ V})$

The formula for the slope $m$ is:
$m_{\text{series}} = \frac{\Delta V}{\Delta I} = \frac{V_2 - V_1}{I_2 - I_1}$
Substitute the values:
$m_{\text{series}} = \frac{2.00 \text{ V} - 0.40 \text{ V}}{0.10 \text{ A} - 0.02 \text{ A}}$ $m_{\text{series}} = \frac{1.60 \text{ V}}{0.08 \text{ A}}$ $m_{\text{series}} = 20 \frac{\text{V}}{\text{A}}$
The slope of the V-I graph represents the resistance.
The slope for the series circuit is $\boxed{\text{20 } \Omega}$ .

Graph for Parallel Data
Prepare the graph axes for Parallel
Draw a horizontal axis (x-axis) for Current $I$ (in Amperes, A) and a vertical axis (y-axis) for Voltage $V$ (in Volts, V).
- For the x-axis (Current), choose a scale that covers $0.05 \text{ A}$ to $0.25 \text{ A}$ .
- For the y-axis (Voltage), choose a scale that covers $0.20 \text{ V}$ to $0.60 \text{ V}$ .
Plot the data points for Parallel
Plot the following points on your graph paper:
- $(0.05 \text{ A}, 0.20 \text{ V})$
- $(0.10 \text{ A}, 0.30 \text{ V})$
- $(0.15 \text{ A}, 0.40 \text{ V})$
- $(0.20 \text{ A}, 0.50 \text{ V})$
- $(0.25 \text{ A}, 0.60 \text{ V})$
Draw the best-fit line for Parallel
Draw a straight line that passes through all the plotted points.
Determine the slope for Parallel
To calculate the slope, choose two distinct points on the best-fit line. We will use the first and last data points.
Point 1: $(I_1, V_1) = (0.05 \text{ A}, 0.20 \text{ V})$
Point 2: $(I_2, V_2) = (0.25 \text{ A}, 0.60 \text{ V})$

The formula for the slope $m$ is:
$m_{\text{parallel}} = \frac{\Delta V}{\Delta I} = \frac{V_2 - V_1}{I_2 - I_1}$
Substitute the values:
$m_{\text{parallel}} = \frac{0.60 \text{ V} - 0.20 \text{ V}}{0.25 \text{ A} - 0.05 \text{ A}}$ $m_{\text{parallel}} = \frac{0.40 \text{ V}}{0.20 \text{ A}}$ $m_{\text{parallel}} = 2 \frac{\text{V}}{\text{A}}$
The slope of the V-I graph represents the resistance.
The slope for the parallel circuit is $\boxed{\text{2 } \Omega}$ .

Draw a graph of Voltage vs. Current for the given series data and calculate its slope.

Step-by-step solution

Graph for Series Data

Prepare the graph axes for Series

Plot the data points for Series

Draw the best-fit line for Series

Determine the slope for Series

Graph for Parallel Data

Prepare the graph axes for Parallel

Plot the data points for Parallel

Draw the best-fit line for Parallel

Determine the slope for Parallel

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