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Plot a graph with voltage (V) on the vertical axis and current (I) on the horizontal axis. (ii) Determine the slope of the graph. (iii) State the significance of the slope.

Physics

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Answer

b(ii)

5.0 Ω5.0 \, \Omega

Step-by-step solution

3 steps

Part a

The tabulated results are:

Current (I) / A0.100.200.300.400.50
Voltage (V) / V0.501.001.502.002.50

Part b(i)

To plot the graph

  1. Draw two perpendicular axes.
  2. Label the vertical axis "Voltage (V)" and the horizontal axis "Current (I)".
  3. Choose appropriate scales for both axes. For example, for current, 1 cm could represent 0.05 A, and for voltage, 1 cm could represent 0.25 V.
  4. Plot each pair of (Current, Voltage) readings as a point on the graph: (0.10, 0.50), (0.20, 1.00), (0.30, 1.50), (0.40, 2.00), (0.50, 2.50).
  5. Draw a straight line of best fit through the plotted points.

Part b(ii)

5.0 Ω5.0 \, \Omega

To determine the slope of the graph

  1. Choose two distinct points on the straight line of best fit.

    Using the points from the table, for example, (I1,V1)=(0.10 A,0.50 V)(I_1, V_1) = (0.10 \text{ A}, 0.50 \text{ V}) and (I2,V2)=(0.50 A,2.50 V)(I_2, V_2) = (0.50 \text{ A}, 2.50 \text{ V}).

  2. Calculate the change in voltage (ΔV\Delta V) and the change in current (ΔI\Delta I).

    ΔV=V2−V1=2.50 V−0.50 V=2.00 V\Delta V = V_2 - V_1 = 2.50 \text{ V} - 0.50 \text{ V} = 2.00 \text{ V} ΔI=I2−I1=0.50 A−0.10 A=0.40 A\Delta I = I_2 - I_1 = 0.50 \text{ A} - 0.10 \text{ A} = 0.40 \text{ A}

  3. Calculate the slope using the formula Slope=ΔVΔI\text{Slope} = \frac{\Delta V}{\Delta I}.

    Slope=2.00 V0.40 A=5.0VA\text{Slope} = \frac{2.00 \text{ V}}{0.40 \text{ A}} = 5.0 \frac{\text{V}}{\text{A}} Slope=5.0 Ω\text{Slope} = \boxed{5.0 \, \Omega}

Part b(iii)

The significance of the slope

The slope of the Voltage (V) versus Current (I) graph represents the resistance of the conductor.

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