Electrical Energy & Power 🔌⚡

1. What happens to a charge that moves through a conductor?

Imagine a charge Q starting at point A (potential V(A)) and ending at point B (potential V(B)). Because current flows from A ➜ B, we have V(A) > V(B). In a short time Δt, the charge ΔQ = I Δt slides from A to B, and its potential-energy change is \( \Delta U_{\text{pot}} = \Delta Q\,[V(B)-V(A)] = – I\,V\,\Delta t \) (3.28):contentReference[oaicite:0]{index=0} A negative sign tells us the charge loses potential energy.

2. Kinetic energy vs. collisions ⚽

  • If the charge zipped along without bumping into atoms, conservation of energy would force its kinetic-energy change to be the exact opposite: \( \Delta K = -\Delta U_{\text{pot}} = I\,V\,\Delta t \) (3.29–3.30):contentReference[oaicite:1]{index=1}
  • Real conductors are full of collisions. Each bump hands energy to the lattice, making it vibrate more—that’s heat! 🔥

3. Heating the wire

During Δt, the energy dumped as heat is \( \Delta W = I\,V\,\Delta t \) (3.31):contentReference[oaicite:2]{index=2} Divide by Δt to get the power (energy per second): \( P = \dfrac{\Delta W}{\Delta t} = I\,V \) (3.32):contentReference[oaicite:3]{index=3}

4. Ohm’s law & three handy power formulas 💡

Hook up Ohm’s law (V = I R) and you unlock two more faces of the same idea: \( P = I^2\,R = \dfrac{V^2}{R} \) (3.33):contentReference[oaicite:4]{index=4} These equations let you pick whichever pair of variables you know—I & R, I & V, or V & R.

5. Where does the energy really come from? 🔋

An external source (a cell, generator, etc.) must constantly supply chemical or mechanical energy. In the simple lamp circuit, the cell’s chemistry feeds exactly the power P that the filament turns into heat and light.:contentReference[oaicite:5]{index=5}

6. Power transmission & the “high-voltage trick” 🏭➡️🏠

Suppose you need to deliver power P to a factory via long cables of total resistance Rc. Inside the factory: \( P = V\,I \) (3.34):contentReference[oaicite:6]{index=6} In the cables, wasted power is \( P_c = I^{2}\,R_{c} = \dfrac{P^{2}\,R_{c}}{V^{2}} \) (3.35):contentReference[oaicite:7]{index=7} Because \(P_c \propto \tfrac{1}{V^{2}}\), boosting the transmission voltage slashes losses. That’s why overhead lines carry scary-high voltages ⚠️. Near homes, transformers step the voltage back down to safe levels before you plug in your phone.

NEET High-Yield Nuggets 🎯

  • Energy lost as heat in a resistor: \( \Delta W = I\,V\,\Delta t \) and \( P = I\,V \).
  • Three interchangeable power formulas: \( P = I\,V = I^{2}R = \dfrac{V^{2}}{R} \).
  • Transmission loss fact: \( P_c = \dfrac{P^{2}R_c}{V^{2}} \) → higher V means lower loss.
  • Sign convention reminder: A drop in potential (negative \( \Delta U_{\text{pot}} \)) corresponds to a gain in kinetic energy for free-moving charges.
  • Heat in a conductor ultimately traces back to the energy source (battery, generator, etc.), highlighting energy conservation in circuits.