🔥 焦耳定律：电流生热的账本🔥 Joule's Law: The Heat Ledger of Current
上一片说到大功率电器要配粗线，因为细线会发热。这一片把热的账算清楚：电流流过导体，一定会产生热——Q = I²Rt，一条公式记满一本账。Last leaf hinted that high-power appliances need thick wires, because thin wires get hot. This leaf settles the heat account: current through a conductor always makes heat — Q = I²Rt, one formula that keeps the whole ledger.
第 1 步：电热丝为什么发红Step 1: Why the heating wire glows red
先看实验室里最诚实的一条线：通电的电热丝会红。Start with the most honest line in the lab: a powered heating wire glows red.
电流挤过电阻时，电子不断和原子「碰撞」，电能就变成了热能。Q = I²Rt：电流 I 的平方、电阻 R、时间 t，三样越大热越多。看那根电热丝：电流把它烧得通红——这正是电暖器、电吹风的原理。When current squeezes through resistance, electrons keep bumping into atoms, and electrical energy becomes heat. Q = I²Rt: the square of the current, the resistance and the time all add heat. Look at the wire: the current glows it red-hot — exactly how heaters and hair dryers work.
既然电流必产热，那输电线上这笔热账谁来付？Since current always makes heat, who pays the heat bill on a power line?
第 2 步：输电线上的「白丢」Step 2: The pure loss on the power line
输电线的电阻很小，但电流可以很大：热量跟电流的平方成正比，电流翻倍，热就变 4 倍。这些热白白散进空气，是发电厂付钱的「白丢」。所以远距离送电用高压：电压高、电流小，这笔热账就小了。A power line has tiny resistance, but the current can be huge — and heat grows with the square of the current: double the current, quadruple the heat. That heat drifts into the air as a pure loss the power plant pays for. That is why long-distance lines use high voltage: higher voltage means lower current, shrinking this heat bill.
同一个公式，为什么电饭锅求它大、输电线求它小？Same formula — so why does a rice cooker want it big while a power line wants it small?
第 3 步：有用热与浪费热Step 3: Useful heat vs wasted heat
电饭锅、热水壶、电暖器：故意用高电阻的发热丝，把电能变成热来干活（有用热）。输电线：电阻越小越好，热是白丢（浪费热）。防范也靠这条公式：用粗铜线减小 R、不超负荷用大电流、装上保险丝和空气开关——都是为了把 Q 管住。Rice cookers, kettles and heaters use high-resistance elements on purpose, turning electricity into useful heat. Power lines want the smallest resistance — there the heat is pure waste. Prevention follows the same formula: thick copper lowers R, avoid overloading with big currents, and fit fuses or breakers — all to keep Q under control.
🎮 你来当电热实验室管理员（30 秒）🎮 Your turn: run the heating-wire lab (30 seconds)
道理讲完了。拖动电流、电阻、时间滑块，看发热量和热度条怎么变；再把发热量调到正好 200 J 和 900 J。Theory done. Drag the current, resistance and time sliders to watch the heat and temperature bar; then tune the heat to exactly 200 J and 900 J.
一句话记住它：Q = I²Rt——电流的平方、电阻、时间，一起决定电流生的热。Remember it in one line: Q = I²Rt — the square of the current, the resistance and the time decide the heat.
电流过电阻必发热；电流翻倍，热变 4 倍（平方项）Current through resistance always heats; double the current, quadruple the heat (the square)电饭锅、电热器故意发热；输电线发热是浪费，电阻越小越好Cookers and heaters glow on purpose; on power lines heat is waste, so smaller resistance is better防范：粗线减小 R、不超负荷、保险丝/空气开关；远距离高压送电减小电流Prevention: thick wires lower R, never overload, use fuses or breakers; high-voltage lines cut the current
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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