☰ Contents · Physics

Short circuit and safety

Lessons 38–39 · 2 lessons · P.Q. Habibullayev, A. Boydedayev, A.D. Bahromov, J.E. Usarov, K.T. Suyarov, M.K. Yuldasheva. Physics, textbook for Grade 8 of general secondary schools, revised and enlarged 3rd edition. “O‘qituvchi” Publishing and Printing Creative House, Tashkent, 2019
39

Problem solving

Textbook: pp. 111–112
GoalSolve problems on voltage drop and power loss in a transmission line and on wire load.
New words
voltage drop · kuchlanish tushuvipower loss · quvvat isrofiline resistance · liniya qarshiligihigh voltage · yuqori kuchlanish
Explanation

Electrical energy reaches the consumer through wires, and since the wires have a resistance R_l they heat up too. The voltage drop in the wire is U_l = I·R_l, and the voltage at the consumer is that much less than the source voltage: U = U_source − U_l. The power loss in the line is P_l = I²R_l; it depends on the square of the current. So when transmitting the same power, by P = IU a higher voltage means a smaller current and a much smaller loss: energy from power stations is transmitted at high voltage. Wires must have a cross-section suited to the current: if a large current flows in a thin wire, it overheats. Choosing and connecting wires is done by electricians.

Worked examples
Source 220 V, line resistance 0.5 Ω, current 20 A: U_l = 20 · 0.5 = 10 V; at the consumer 220 − 10 = 210 V; loss P_l = 20² · 0.5 = 200 W.
Transmitting 100 kW through a line with R_l = 2 Ω at 1000 V: I = 100000 : 1000 = 100 A, loss 100² · 2 = 20 kW. At 10 000 V: I = 10 A, loss 10² · 2 = 200 W — 100 times less.
Class activity

Make a simple table in your notebook: for the same 50 kW calculate the current (I = P/U) at 500 V and 5000 V and write in which case the loss is smaller.

Practice
1
Why is electrical energy transmitted at high voltage?
2
The line resistance is 1 Ω and the current 15 A. The voltage drop in V?
3
A line has R = 3 Ω and I = 10 A. The power loss in W?
4
Why is it dangerous to run a large current through a thin wire?