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Help me draw a graph with the determination of the slope

Mathematics

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Answer

20 Ω\text{20 } \Omega

Step-by-step solution

4 steps

To draw the graph and determine the slope, we will use the "Series" data provided. In this experiment, Voltage (V) is typically plotted on the y-axis and Current (I) on the x-axis. The slope of the V-I graph represents the resistance (RR).

  1. Prepare the graph axes

    Draw a horizontal axis (x-axis) for Current II (in Amperes, A) and a vertical axis (y-axis) for Voltage VV (in Volts, V). Choose appropriate scales for both axes to accommodate the range of values. For current, the range is from 0.02 A0.02 \text{ A} to 0.10 A0.10 \text{ A}. For voltage, the range is from 0.40 V0.40 \text{ V} to 2.00 V2.00 \text{ V}.

  2. Plot the data points

    Plot the following points on your graph paper:

    • (0.02 A,0.40 V)(0.02 \text{ A}, 0.40 \text{ V})
    • (0.04 A,0.80 V)(0.04 \text{ A}, 0.80 \text{ V})
    • (0.05 A,1.00 V)(0.05 \text{ A}, 1.00 \text{ V})
    • (0.08 A,1.60 V)(0.08 \text{ A}, 1.60 \text{ V})
    • (0.10 A,2.00 V)(0.10 \text{ A}, 2.00 \text{ V})
  3. Draw the best-fit line

    Draw a straight line that passes through or is closest to all the plotted points. Since the data is linear, the line should pass through all points.

  4. Determine the slope

    To calculate the slope, choose two distinct points on the best-fit line. We will use the first and last data points for accuracy.
    Point 1: (I1,V1)=(0.02 A,0.40 V)(I_1, V_1) = (0.02 \text{ A}, 0.40 \text{ V})
    Point 2: (I2,V2)=(0.10 A,2.00 V)(I_2, V_2) = (0.10 \text{ A}, 2.00 \text{ V})

    The formula for the slope mm is:

    m=ΔVΔI=V2−V1I2−I1m = \frac{\Delta V}{\Delta I} = \frac{V_2 - V_1}{I_2 - I_1}

    Substitute the values:

    m=2.00 V−0.40 V0.10 A−0.02 Am = \frac{2.00 \text{ V} - 0.40 \text{ V}}{0.10 \text{ A} - 0.02 \text{ A}} m=1.60 V0.08 Am = \frac{1.60 \text{ V}}{0.08 \text{ A}} m=20VAm = 20 \frac{\text{V}}{\text{A}}

    The unit VA\frac{\text{V}}{\text{A}} is equivalent to Ohms (Ω\Omega).

    The slope of the V-I graph represents the resistance of the circuit.
    The slope is 20 Ω\text{20 } \Omega.

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