iciency/questions","formulaUrl":null,"initialIndex":31,"initialQuestionWindow":[{"id":"ec5aecf4-fb19-4f96-9b9a-4e2fed62620e","revisionId":"e7e43d29-6f64-443c-921c-9a505988d8a1","questionNumber":null,"questionType":"LA","specification":"An electric hot water dispenser is used to heat water.\n\nThe amount of energy, $E$, needed to heat the water is $504\\,000\\text{ J}$.\n\nThe dispenser has a power of $2800\\text{ W}$.","difficulty":3,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"f6f79705-d665-4d2e-98f9-fdf1b43d158e","label":null,"content":"Calculate the time, $t$, it takes to heat the water.\n\nUse the equation:\n$$P = \\frac{E}{t}$$","markscheme":"- Rearranges the formula to $t = \\frac{E}{P}$ OR substitutes values into the original formula to get $2800 = \\frac{504\\,000}{t}$ M1\n- Sets up the correct calculation: $t = \\frac{504\\,000}{2800}$ M1\n- Obtains $180$ (s) A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"rearrange_formula","label":"Rearrange the formula","steps":[{"type":"text","order":0,"title":"Identify each quantity","content":"Use $P=\\frac{E}{t}$, where $P$ is power in watts, $E$ is energy in joules and $t$ is time in seconds. Here, $E=504\\,000\\text{ J}$ and $P=2800\\text{ W}$.\n\nThe units already match the equation, so no conversion is needed.","highlights":[{"text":"The amount of energy, $E$, needed to heat the water is $504\\,000\\text{ J}$.","location":"specification"},{"text":"The dispenser has a power of $2800\\text{ W}$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"P=\\frac{E}{t}"},{"latex":"Pt=E"},{"latex":"t=\\frac{E}{P}"}]},"order":1,"title":"Make time the subject","description":"Time is underneath the fraction bar. Multiply both sides by t, then divide both sides by P. This rearrangement earns the first method mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"t=\\frac{E}{P}"},{"latex":"t=\\frac{504\\,000}{2800}"}]},"order":2,"title":"Substitute the values","description":"Put the energy on top and the power on the bottom. Setting up this calculation earns the second method mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"t=\\htmlData{anchor=calculation}{\\frac{504\\,000}{2800}}"},{"latex":"t=\\htmlData{anchor=answer}{180\\text{ s}}"}],"highlights":[{"color":"green","style":"box","anchor":"answer"}],"connections":[{"to":"answer","from":"calculation","color":"green","label":"calculate"}]},"order":3,"title":"Calculate the time","description":"Obtaining 180 s earns the accuracy mark."}]}],"generatedAt":"2026-07-22T09:32:39.537Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"f602f505-c8d9-4738-bc77-1ba749a7a4de","revisionId":"29c56991-e540-4083-bdbd-142b81f1aea6","questionNumber":null,"questionType":"LA","specification":"A student investigates the power output of three different model electric motor systems, X, Y, and Z, lifting a load. The results are shown in the table below.\n\n| Model | Pulling force in N | Distance in m | Work done in J | Time taken in s | Power in W |\n| :--- | :---: | :---: | :---: | :---: | :---: |\n| X | 20.5 | 4.0 | 82.0 | 5.0 | 16.4 |\n| Y | | 4.0 | 90.5 | 5.0 | 18.1 |\n| Z | 13.5 | 4.0 | 54.0 | | 13.5 |","difficulty":2,"difficultyBand":"easy","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"e9900823-f15d-4777-8e7b-80670c50c3a9","label":null,"content":"Use the data for all three models to calculate their average power.","markscheme":"- Substitutes the power values from the table into the average power formula: $\\dfrac{16.4 + 18.1 + 13.5}{3}$ or $\\dfrac{48.0}{3}$ M1\n- Obtains a final average power of $16.0$ W or $16$ W A1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"mean_power","label":"Calculate the mean power","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"16.4\\ \\mathrm{W}+18.1\\ \\mathrm{W}+

Power and efficiency

Question 21

Power and efficiency Questions

Power and efficiency

Question 21

Power and efficiency Questions