iency/questions","formulaUrl":null,"initialIndex":0,"initialQuestionWindow":[{"id":"10bc88ed-290c-4303-8a6a-5e4877ea0b96","revisionId":"f1dfd1c7-cf71-48ad-aabf-a57cbd1ed3c0","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"e4739dc1-b6ea-43d7-9227-0f5e9d89044e","label":null,"content":"An electric shower transfers $165\\text{ }000\\text{ J}$ of energy to the water flowing through it in a time of $45\\text{ s}$.\n\nCalculate the power transferred by the electric shower.\n\nUse the equation:\n$$P = \\frac{E}{t}$$\n\nGive your answer to 2 significant figures.","markscheme":"- Substitutes correct values into the power equation: $P = \\frac{165\\text{ }000}{45}$ M1\n- Evaluates the intermediate calculation to get $3666.67$ (or $3667$) A1\n- Rounds the final answer to 2 significant figures with correct units: $3700\\text{ W}$ (or $3.7\\text{ kW}$) A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"use_power_equation","label":"Use the power equation","steps":[{"type":"text","order":0,"title":"Identify the quantities","content":"The energy transferred is $E=165\\,000\\ \\text{J}$ and the time taken is $t=45\\ \\text{s}$. Power means the energy transferred each second, so use the equation given:\n\n$$P=\\frac{E}{t}$$","highlights":[{"text":"transfers $165\\text{ }000\\text{ J}$ of energy","location":"specification"},{"text":"time of $45\\text{ s}$","location":"specification"},{"text":"$$$P = \\frac{E}{t}$$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"P=\\frac{E}{t}"},{"latex":"P=\\frac{\\htmlData{anchor=energy}{165\\,000}}{\\htmlData{anchor=time}{45}}"},{"latex":"P=\\htmlData{anchor=calculated}{3666.67\\ \\mathrm{W}}"},{"text":"Evaluating 165 000 ÷ 45 = 3666.67 W earns the intermediate A1 mark."}],"highlights":[{"color":"green","style":"box","anchor":"calculated"}]},"order":1,"title":"Substitute the values","description":"Put the energy in joules and the time in seconds into the equation. This substitution earns the M1 mark."},{"type":"text","order":2,"title":"Round the answer","content":"To 2 significant figures, $3666.67\\ \\text{W}$ becomes $3700\\ \\text{W}$: keep the first two digits, $3$ and $6$, then round up because the next digit is $6$.\n\n$$\\boxed{P=3700\\ \\text{W}}$$\n\nThis earns the final A1 mark. Equivalently, $3700\\ \\text{W}=3.7\\ \\text{kW}$.","highlights":[{"text":"Give your answer to 2 significant figures.","location":"specification"}]}]}],"generatedAt":"2026-07-22T09:31:32.407Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"13423822-2b89-4d19-b0d8-838855ba1aed","revisionId":"9d4a5f87-be8f-4db9-900b-a4eefa877b0e","questionNumber":null,"questionType":"LA","specification":"An industrial drainage pump is used to lift wastewater from a deep holding tank. The useful work done against gravity in raising the wastewater is $14.7\\text{ MJ}$.\n\nThe overall efficiency of the pump system is $42\\%$.","difficulty":4,"difficultyBand":"easy","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"dc9b11c4-0128-432e-ab51-08354172a7aa","label":null,"content":"Calculate the total work done by the pump's electric motor to complete this operation.\n\nUse the equation:\n$$\\text{efficiency} = \\frac{\\text{useful work done}}{\\text{total work done by the motor}} \\times 100\\%$$","markscheme":"- Rearranges the efficiency equation or substitutes the given values, e.g. $\\text{total work done} = \\frac{14.7}{0.42}$ or $42 = \\frac{14.7}{\\text{total work}} \\times 100$ M1\n- Obtains the correct total work done of $35\\text{ MJ}$ (or $35\\text{,000}\\text{ kJ}$ / $3.5 \\times 10^7\\text{ J}$) A1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"efficiency_equation","label":"Rearrange the efficiency equation","steps":[{"type":"text

Power and efficiency

Question 1

Power and efficiency Questions

Power and efficiency

Question 1

Power and efficiency Questions