{"job_id":"anim-job-cbdd7ca3-e4d6-44d4-b271-411a91eda098","request_id":"test-physics-capacitor-ba30c5e5-e5bb-4ff3-90a7-a40b2e480a51-1778708287067","status":"complete","asset":{"primary_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-cbdd7ca3-e4d6-44d4-b271-411a91eda098/walkthrough.mp4","thumbnail_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-cbdd7ca3-e4d6-44d4-b271-411a91eda098/thumb.jpg","transcript_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-cbdd7ca3-e4d6-44d4-b271-411a91eda098/transcript.vtt","interactive_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-cbdd7ca3-e4d6-44d4-b271-411a91eda098/index.html","scenefile_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-cbdd7ca3-e4d6-44d4-b271-411a91eda098/scene-source.json","duration_seconds":15,"byte_size":468032,"renderer":"html_three_js_local","parameters":{"style":"auto","executor":"native_render_executor","localPath":"/app/storage/assets/anim-job-cbdd7ca3-e4d6-44d4-b271-411a91eda098","interactivity":"none","renderer_style":"three_js","durationSeconds":15,"render_manifest":{"jobId":"anim-job-cbdd7ca3-e4d6-44d4-b271-411a91eda098","request":{"gap":{"topic":"capacitor-charging-curve","severity":"dangerous","error_type":"concept_misunderstanding","memory_state":"fragile","display_topic":"Capacitor Charging in an RC Circuit","common_wrong_answer":"A capacitor charges linearly at a constant rate.","confidence_at_error":"high","correct_understanding":"Capacitor charges exponentially: V(t) = V₀(1 − e^(−t/RC)). Rate slows as charge builds up."},"target":{"style":"auto","render":{"fps":30,"format":"mp4","resolution":"1920x1080","include_thumbnail":true,"include_transcript":true},"audience":{"tone":"neutral_instructional","grade":"12","language":"en"},"interactivity":"none","duration_seconds":15},"context":{"chapter":{"name":"Electrostatic Potential and Capacitance","ncert_class":12,"ncert_chapter_number":2},"sub_topics":[{"topic":"Capacitor","key_concepts":["capacitance","charging","RC circuit","time constant"]}]},"metadata":{"priority":"normal"},"exam_type":"neet","asset_type":"simulation","request_id":"test-physics-capacitor-ba30c5e5-e5bb-4ff3-90a7-a40b2e480a51-1778708287067","subject_area":"physics"},"renderer":"html_three_js_local","storyboard":{"beats":[{"label":"Topic","visual":"Show the topic title and the key physical context.","narration":"Capacitor Charging in an RC Circuit"},{"label":"Mistake","visual":"Show the wrong approach and why it seems plausible.","narration":"A capacitor charges linearly at a constant rate."},{"label":"Correction","visual":"Show the right approach step by step.","narration":"Capacitor charges exponentially: V(t) = V₀(1 − e^(−t/RC)). Rate slows as charge builds up."},{"label":"Concept","visual":"Highlight the key formula and the governing relationship.","narration":"capacitance. charging. RC circuit"}],"title":"Capacitor Charging in an RC Circuit","sceneCode":"<!doctype html>\n<html lang=\"en\">\n<head>\n  <meta charset=\"utf-8\"/>\n  <meta name=\"viewport\" content=\"width=device-width, initial-scale=1\"/>\n  <title>RC Capacitor Charging: Linear vs. Exponential</title>\n  <style>\n    :root{--bg:#0f1418;--panel:#182228;--line:#2e3e46;--accent:#e5ba67;--text:#f4f1ea;--muted:#c8d4da;--blue:#63b3ff;--green:#87e8a8;--red:#de7f76;}\n    *{box-sizing:border-box;}\n    body{margin:0;font-family:\"Plus Jakarta Sans\",\"Manrope\",\"Inter\",ui-sans-serif,system-ui,sans-serif;background:radial-gradient(120% 90% at 20% -5%,#24343d 0%,var(--bg) 55%);color:var(--text);}\n    main{min-height:100vh;display:grid;grid-template-columns:minmax(300px,380px) 1fr;}\n    aside{border-right:1px solid var(--line);background:linear-gradient(180deg,rgba(31,46,53,.86),rgba(24,34,40,.92));padding:24px;overflow:auto;backdrop-filter:blur(6px);}\n    section{padding:24px;display:grid;place-items:center;}\n    h1{margin:0 0 10px;font-size:1.65rem;line-height:1.15;}\n    .sub{margin:0 0 16px;color:var(--muted);}\n    .formula{margin:0 0 14px;padding:10px;border:1px solid var(--line);border-radius:10px;background:#11191e;color:var(--accent);font-family:ui-monospace,monospace;font-size:0.9rem;box-shadow:inset 0 0 28px rgba(229,186,103,.08);}\n    .control{display:grid;gap:6px;margin:12px 0;}\n    .control input{width:100%;accent-color:var(--accent);}\n    ul{margin:14px 0 0 18px;padding:0;color:var(--muted);display:grid;gap:6px;}\n    .stage{width:min(1020px,95%);aspect-ratio:16/9;border:1px solid #445862;border-radius:14px;position:relative;overflow:hidden;background:radial-gradient(circle at 50% 38%,#2f4a57,#0f1418 72%);box-shadow:0 18px 60px rgba(0,0,0,.45), inset 0 0 90px rgba(255,255,255,.03);}\n    .stage::before{content:\"\";position:absolute;inset:0;background:linear-gradient(180deg,rgba(255,255,255,.06),transparent 34%);pointer-events:none;}\n    .legend{position:absolute;right:12px;top:12px;padding:8px 10px;border-radius:10px;border:1px solid #465a64;background:rgba(9,14,18,.58);font-size:0.8rem;color:var(--muted);backdrop-filter:blur(4px);}\n    @media(max-width:900px){main{grid-template-columns:1fr;}aside{border-right:0;border-bottom:1px solid var(--line);}}\n  </style>\n</head>\n<body>\n<main>\n  <aside>\n    <h1>RC Charging</h1>\n    <p class=\"sub\">Linear (Wrong) vs. Exponential (Right)</p>\n    <p class=\"formula\">V(t) = V₀(1 − e^(−t/RC))</p>\n    <label class=\"control\"><span>Time Constant RC (s): <strong id=\"v-rc\">0.8</strong></span><input id=\"c-rc\" type=\"range\" min=\"0.3\" max=\"2\" step=\"0.1\" value=\"0.8\"/></label>\n    <label class=\"control\"><span>Supply Voltage V₀ (V): <strong id=\"v-v0\">5</strong></span><input id=\"c-v0\" type=\"range\" min=\"3\" max=\"10\" step=\"1\" value=\"5\"/></label>\n    <label class=\"control\"><span>Animation Speed: <strong id=\"v-speed\">1</strong>×</span><input id=\"c-speed\" type=\"range\" min=\"0.3\" max=\"2\" step=\"0.1\" value=\"1\"/></label>\n    <ul>\n      <li><strong>❌ Misconception:</strong> Capacitor fills linearly with constant current.</li>\n      <li><strong>✓ Reality:</strong> Charging slows exponentially as charge builds.</li>\n      <li><strong>⚡ Key:</strong> Back-EMF opposes charging; rate ∝ (V₀−V).</li>\n      <li><strong>📈 Watch:</strong> Red line (wrong) goes straight; blue (correct) curves.</li>\n    </ul>\n  </aside>\n  <section>\n    <div class=\"stage\" id=\"stage\">\n      <div class=\"legend\" id=\"legend\">Ready</div>\n      <canvas id=\"sim-cv\" style=\"position:absolute;inset:0;width:100%;height:100%;\"></canvas>\n    </div>\n  </section>\n</main>\n<script>\nconst controls = [\n  {\"key\":\"rc\",\"label\":\"Time Constant RC\",\"min\":0.3,\"max\":2,\"step\":0.1,\"value\":0.8,\"units\":\"s\"},\n  {\"key\":\"v0\",\"label\":\"Supply Voltage V₀\",\"min\":3,\"max\":10,\"step\":1,\"value\":5,\"units\":\"V\"},\n  {\"key\":\"speed\",\"label\":\"Animation Speed\",\"min\":0.3,\"max\":2,\"step\":0.1,\"value\":1,\"units\":\"×\"}\n];\nfor(const c of controls){\n  const inp=document.getElementById('c-'+c.key);\n  const out=document.getElementById('v-'+c.key);\n  inp?.addEventListener('input',()=>{out.textContent=inp.value;window.updateModel?.();});\n}\n(function(){\n  const cv=document.getElementById('sim-cv');\n  const ctx=cv.getContext('2d');\n  function resize(){const r=cv.getBoundingClientRect();if(r.width>0){cv.width=r.width;cv.height=r.height;}}\n  resize();new ResizeObserver(resize).observe(cv);\n  \n  // State variables\n  let t = 0;\n  const linearTrail = [];\n  const exponentialTrail = [];\n  const maxTrailLen = 200;\n  \n  let lastTs = 0;\n  \n  function glowDot(x, y, r, color, a) {\n    const g = ctx.createRadialGradient(x, y, 0, x, y, r * 2.6);\n    g.addColorStop(0, color.replace('ALPHA', String(a)));\n    g.addColorStop(1, color.replace('ALPHA', '0'));\n    ctx.fillStyle = g;\n    ctx.beginPath();\n    ctx.arc(x, y, r * 2.6, 0, Math.PI * 2);\n    ctx.fill();\n  }\n  \n  function trail(points, color) {\n    if (points.length < 2) return;\n    ctx.strokeStyle = color;\n    ctx.lineWidth = 2.5;\n    ctx.globalAlpha = 0.7;\n    ctx.beginPath();\n    ctx.moveTo(points[0].x, points[0].y);\n    for (let i = 1; 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// Wrong: linear growth\n    const V_exponential = V0 * (1 - Math.exp(-t / RC)); // Correct: exponential\n    \n    const V_lin_clamped = Math.min(V_linear, V0);\n    const V_exp_clamped = Math.min(V_exponential, V0);\n    \n    // Layout\n    const graphLeft = W * 0.08;\n    const graphRight = W * 0.92;\n    const graphTop = H * 0.12;\n    const graphBottom = H * 0.78;\n    const graphWidth = graphRight - graphLeft;\n    const graphHeight = graphBottom - graphTop;\n    \n    // Time axis scale\n    const tMax = RC * 4;\n    const xScale = (time) => graphLeft + (time / tMax) * graphWidth;\n    const yScale = (v) => graphBottom - (v / V0) * graphHeight;\n    \n    // Add trail points\n    if (linearTrail.length === 0 || Math.abs(t - linearTrail[linearTrail.length - 1].t) > 0.01) {\n      linearTrail.push({ x: xScale(t), y: yScale(V_lin_clamped), t: t });\n      exponentialTrail.push({ x: xScale(t), y: yScale(V_exp_clamped), t: t });\n      if (linearTrail.length > maxTrailLen) {\n        linearTrail.shift();\n        exponentialTrail.shift();\n      }\n    }\n    \n    // Clear background\n    ctx.clearRect(0, 0, W, H);\n    \n    // === Background layers ===\n    ctx.fillStyle = 'rgba(15, 20, 24, 0.3)';\n    ctx.fillRect(0, 0, W, H);\n    \n    // === Grid background ===\n    ctx.strokeStyle = 'rgba(68, 88, 98, 0.15)';\n    ctx.lineWidth = 1;\n    for (let i = 0; i <= 5; i++) {\n      const y = graphTop + (i / 5) * graphHeight;\n      ctx.beginPath();\n      ctx.moveTo(graphLeft, y);\n      ctx.lineTo(graphRight, y);\n      ctx.stroke();\n    }\n    for (let i = 0; i <= 8; i++) {\n      const x = graphLeft + (i / 8) * graphWidth;\n      ctx.beginPath();\n      ctx.moveTo(x, graphTop);\n      ctx.lineTo(x, graphBottom);\n      ctx.stroke();\n    }\n    \n    // === Axes ===\n    ctx.strokeStyle = '#c8d4da';\n    ctx.lineWidth = 2;\n    ctx.beginPath();\n    ctx.moveTo(graphLeft, graphBottom);\n    ctx.lineTo(graphRight, graphBottom);\n    ctx.stroke();\n    ctx.beginPath();\n    ctx.moveTo(graphLeft, graphTop);\n    ctx.lineTo(graphLeft, graphBottom);\n    ctx.stroke();\n    \n    // Axis labels\n    ctx.fillStyle = '#c8d4da';\n    ctx.font = Math.round(H * 0.032) + 'px sans-serif';\n    ctx.textAlign = 'center';\n    ctx.textBaseline = 'top';\n    ctx.fillText('Time (τ)', graphLeft + graphWidth / 2, graphBottom + H * 0.04);\n    \n    ctx.textAlign = 'right';\n    ctx.textBaseline = 'middle';\n    ctx.fillText('Voltage (V)', graphLeft - H * 0.03, graphTop - H * 0.02);\n    \n    // Y-axis tick labels\n    ctx.font = Math.round(H * 0.025) + 'px monospace';\n    ctx.fillStyle = '#c8d4da';\n    for (let i = 0; i <= 5; i++) {\n      const v = (i / 5) * V0;\n      const y = graphBottom - (i / 5) * graphHeight;\n      ctx.textAlign = 'right';\n      ctx.textBaseline = 'middle';\n      ctx.fillText(v.toFixed(1), graphLeft - H * 0.025, y);\n    }\n    \n    // X-axis time labels\n    ctx.fillStyle = '#c8d4da';\n    for (let i = 0; i <= 4; i++) {\n      const tau = i;\n      const x = graphLeft + (i / 4) * graphWidth;\n      ctx.textAlign = 'center';\n      ctx.textBaseline = 'top';\n      ctx.fillText(tau + 'τ', x, graphBottom + H * 0.012);\n    }\n    \n    // === Draw trails ===\n    trail(linearTrail, '#de7f76');\n    trail(exponentialTrail, '#63b3ff');\n    \n    // === Draw current points ===\n    const xLin = xScale(t);\n    const yLin = yScale(V_lin_clamped);\n    const xExp = xScale(t);\n    const yExp = yScale(V_exp_clamped);\n    \n    // Linear point (wrong)\n    glowDot(xLin, yLin, 6, 'rgba(222, 127, 118, ALPHA)', 0.8);\n    ctx.fillStyle = '#de7f76';\n    ctx.beginPath();\n    ctx.arc(xLin, yLin, 5, 0, Math.PI * 2);\n    ctx.fill();\n    \n    // Exponential point (correct)\n    glowDot(xExp, yExp, 6, 'rgba(99, 179, 255, ALPHA)', 0.8);\n    ctx.fillStyle = '#63b3ff';\n    ctx.beginPath();\n    ctx.arc(xExp, yExp, 5, 0, Math.PI * 2);\n    ctx.fill();\n    \n    // === Voltage indicator bars below graph ===\n    const barY = graphBottom + H * 0.15;\n    const barH = H * 0.06;\n    const barW = graphWidth * 0.18;\n    const bar1X = graphLeft;\n    const bar2X = graphLeft +","remediationGoal":"Close concept_misunderstanding for physics."},"rendererStyle":"three_js"}}},"metadata":{"rendered_at":"2026-05-13T21:42:19.554Z","cache_hit":false,"cost_usd":0},"error":null}