In an experiment to verify Joule's law a constant current was passed through a heating coil immersed in water - Leaving Cert Physics - Question 5 - 2021

The current was allowed to flow for a constant period of time to:

• Maintain Experimental Consistency: Keeping the time constant ensures that the measurements for temperature rise are directly comparable.
• Eliminate Time as a Variable: This allows for a more accurate analysis of how changes in current affect the temperature rise without the influence of varying time durations.

To verify Joule's law:

1. Values for I² (current squared): Calculate I² for the given currents:

   • I = 1.0 A; I² = 1.0
   • I = 1.5 A; I² = 2.25
   • I = 2.0 A; I² = 4.0
   • I = 2.5 A; I² = 6.25
   • I = 3.0 A; I² = 9.0
   • I = 3.5 A; I² = 12.25

2. Labelled Axes: Label the x-axis as 'I² (A²)' and the y-axis as 'ΔΘ (°C)'.

3. Correct Points Plotted: Plot the calculated points on the graph.

4. Line of Best Fit: Draw a line of best fit to illustrate the relationship between I² and ΔΘ, confirming Joule's law.

To calculate the resistance:

1. Slope Formula: Use the slope formula where slope = rac{ ext{ΔΘ}}{ ext{I²}}.

2. Value of Slope: Assume the value of the slope calculated from the graph is 2.03.

3. Using Joule's Law: Apply the relation: P = R rac{ΔΘ}{mcΔt} where

   • $P$ is the power,
   • $R$ is the resistance,
   • $m$ is the mass of water (0.105 kg),
   • $c$ is the specific heat capacity of water (4180 J/kg·K),
   • $Δt$ is the time duration in seconds (240 s).

4. Calculate Resistance: Rearranging gives: R = rac{m c imes ext{slope}}{P} Substituting the values will yield: $R ext{ is approximately } 3.71 ext{ Ω}$