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Using the provided graph, estimate V when I = 10.0 A, estimate I when V = 8.0 V, and determine the slope and relationship between I and V.

Physics

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Here are the solutions to Question 7.

Question 7:

  • I. Estimate the value of V when I is 10.0 amperes.

  1. Locate I=10.0I = 10.0 amperes on the vertical (I) axis.

  2. Move horizontally from I=10.0I = 10.0 A to the right until you intersect the line of best fit.

  3. From the intersection point, move vertically downwards to the horizontal (V) axis.

  4. Read the value on the V-axis.

    $$
V = \boxed{5.0 \text{ volts}}
$$
    • II. Estimate the value of I when V is 8.0 volts.

  5. Locate V=8.0V = 8.0 volts on the horizontal (V) axis.

  6. Move vertically upwards from V=8.0V = 8.0 V until you intersect the line of best fit.

  7. From the intersection point, move horizontally to the left to the vertical (I) axis.

  8. Read the value on the I-axis.

    $$
I = \boxed{16.0 \text{ amperes}}
$$
    • III. Determine the graph slope and write down the mathematical relation between I and V.

  9. Choose two distinct points on the line of best fit.

    For accuracy, choose points far apart. Let's use (V1,I1)=(0 V,0 A)(V_1, I_1) = (0 \text{ V}, 0 \text{ A}) and (V2,I2)=(10.0 V,20.0 A)(V_2, I_2) = (10.0 \text{ V}, 20.0 \text{ A}).

  10. Calculate the slope (mm) using the formula m=I2−I1V2−V1m = \frac{I_2 - I_1}{V_2 - V_1}.

    $$
m = \frac{20.0 \text{ A} - 0 \text{ A}}{10.0 \text{ V} - 0 \text{ V}}
$$
$$
m = \frac{20.0 \text{ A}}{10.0 \text{ V}}
$$
$$
\text{Slope} = \boxed{2.0 \text{ A/V}}
$$

  11. Write down the mathematical relation.

    Since the line passes through the origin, the relation is of the form I=mVI = m V. Mathematical relation:I=2.0V \text{Mathematical relation:} \boxed{I = 2.0 V}

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