Derive an expression for the power dissipated in a resistor carrying a current. Show why electric power is transmitted over long distances at high voltage.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · State the idea. Electric power is the rate at which a resistor turns electrical energy into heat: P = ΔW/Δt.
2 · Charge and energy. In time Δt, a charge ΔQ = IΔt falls through a potential difference V and loses potential energy ΔQ V = IVΔt. Collisions pass it to the ions as heat.
3 · Find the power. P = ΔW/Δt = VI. With V = IR: P = I²R = V²/R.
4 · Draw the diagram. [Conductor AB with current I from A to B, V(A) > V(B), and a cell joined across it]
5 · Transmission. Cables of resistance R_c carry I = P/V, so the loss is P_c = I²R_c = P²R_c/V².
6 · Real life. So transmission lines in India run at hundreds of kilovolts, and transformers step the voltage down to 220 V near homes.
7 · Close in one line. So, P = VI = I²R = V²/R, and a high V means a small I and a small I²R loss.
Scoring tip: After writing P_c = P²R_c/V², say it in words: the loss falls as the square of the voltage.
