Physics: Energy, Work, and Electricity
Energy questions combine a work calculation with a circuit or a heating experiment, so the units must be automatic.
Work and energy
- 仕事 (J) = force (N) × distance moved in the direction of the force (m).
- No work is done when the force is perpendicular to the motion, as when a bag is carried horizontally or held still.
- 仕事率 (W) = 仕事 ÷ 時間.
- 力学的エネルギー = 位置エネルギー + 運動エネルギー. 位置エネルギー is proportional to mass and height; 運動エネルギー is proportional to mass and to the square of speed.
- 力学的エネルギー保存の法則 holds only when friction and air resistance are negligible.
Circuits
- オームの法則: V = R I.
- 直列: current is equal everywhere, voltages add, R = R₁ + R₂.
- 並列: voltage is equal across branches, currents add, and the combined resistance is smaller than either resistor.
- 電力 P = V I (W); 電力量 = P × t, in J (W·s) or Wh, where 1 Wh = 3600 J.
Worked example. A 6.0 V supply drives a 3.0 Ω heater for 5.0 minutes. I = 6.0 ÷ 3.0 = 2.0 A; P = 6.0 × 2.0 = 12 W; t = 300 s, so energy = 12 × 300 = 3600 J = 1.0 Wh. If this heats 100 g of water with no loss, ΔT = 3600 ÷ (4.2 × 100) ≈ 8.6 K.
Traps. Giving 電力量 in W instead of J or Wh; adding parallel resistors as if in series; assuming a resistor's value changes with voltage; forgetting the 3600 conversion; writing 仕事 for a force whose point of application does not move.