lIndex":11,"initialQuestionWindow":[{"id":"3dbaf5ff-320e-4663-931d-6d6155b42dce","revisionId":"18ebcb15-e168-43f0-9055-36c733343005","questionNumber":null,"questionType":"LA","specification":"Six identical indicator lamps are connected in series to a $24\\text{ V}$ power supply.\n\n![A circuit diagram showing six identical indicator lamps connected in series across a 24 V DC power supply source.](https://assets.mathsgenie.co.uk/aqa-qb/7de4e1fe-ba84-472c-84ce-45640e403b4e.png)\n\nThe power output of each lamp is $1.6\\text{ W}$.","difficulty":5,"difficultyBand":"medium","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"4e582a32-cc82-4bc0-ac81-6f13963967ab","label":null,"content":"Calculate the resistance of each lamp.","markscheme":"- Calculates the potential difference across a single lamp as $V = \\frac{24}{6} = 4\\text{ V}$ B1\n- Applies a correct formula relating power, voltage, and resistance, e.g. $P = \\frac{V^2}{R}$ or calculates current $I = \\frac{P}{V} = 0.4\\text{ A}$ M1\n- Calculates the correct numerical value of resistance as $10$ A1\n- States the correct unit of resistance as $\\Omega$ or ohms B1","marks":4,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"use_power_equation","label":"Use the power equation","steps":[{"type":"text","order":0,"title":"Share the supply voltage","content":"The lamps are **identical** and connected in series, so the $24\\ \\mathrm{V}$ supply is shared equally between all six lamps.\n\n$$V_{\\text{lamp}}=\\frac{24}{6}=4\\ \\mathrm{V}$$\n\nThis earns the first **B1** mark.","highlights":[{"text":"Six identical indicator lamps are connected in series to a $24\\text{ V}$ power supply.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"P = \\htmlData{anchor=power_fraction}{\\frac{V^2}{R}}"},{"latex":"R = \\htmlData{anchor=resistance_form}{\\frac{V^2}{P}}"}],"highlights":[{"color":"amber","style":"box","anchor":"resistance_form"}],"connections":[{"to":"resistance_form","from":"power_fraction","color":"amber","label":"rearrange"}]},"order":1,"title":"Rearrange the power equation","description":"Multiply both sides by R, then divide by P, to make resistance the subject."},{"type":"hyper_latex","block":{"nodes":[{"latex":"R = \\frac{V^2}{P}"},{"latex":"R = \\frac{(4)^2}{1.6}"},{"latex":"R = \\htmlData{anchor=answer}{10\\ \\Omega}"}],"highlights":[{"color":"green","style":"box","anchor":"answer"}]},"order":2,"title":"Substitute the lamp values","description":"Substitute the voltage and power for one lamp. Using P = V²/R earns M1; R = 10 ohms earns A1 and B1."}]}],"generatedAt":"2026-07-22T09:39:16.667Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"3e0a1b73-d369-4bd4-84dc-443b5400a4fd","revisionId":"29d71b25-54c1-4678-bdb5-845c39b6d6fb","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"3dc47f95-7d00-4ee9-bd7a-e0850cb39603","label":null,"content":"An electric scooter motor is connected to a $36\\text{ V}$ battery pack. Over a climb lasting $8\\text{ minutes}$, it transfers $129\\,600\\text{ J}$ of electrical energy.\n\nCalculate the current in the motor during this climb.\n\nUse the equation:\n$$I = \\frac{E}{V \\times t}$$","markscheme":"- Converts time from minutes to seconds: $8 \\times 60 = 480\\text{ s}$ M1\n- Substitutes values into the given equation: $I = \\dfrac{129\\,600}{36 \\times 480}$ M1\n- Calculates the correct current of $7.5\\text{ A}$ A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"substitution","label":"Convert then substitute","steps":[{"type":"text","order":1,"title":"Convert the time","content":"The equation needs $t$ in seconds, so convert the given $8\\text{ minutes}$:\n\n$$8 \\times 60 = 480\\text{ s}$$\n\nWriting this conversion earns **M

Electrical power

Question 5

Electrical power Questions

Electrical power

Question 5

Electrical power Questions