18
Problem solving
Textbook: pp. 60–61
GoalSolve problems using Ohm’s law together with R = ρ·l/S: current, voltage, wire length and cross-section.
New words
wire resistance · sim qarshiligivoltage drop · kuchlanish tushuvitable of resistivities · solishtirma qarshilik jadvalichecking units · birliklarni tekshirish
Explanation
In these problems two formulas form a chain: R = ρ·l/S and I = U/R. If the wire’s parameters (substance, l, S) are given, first find R, then use Ohm’s law for I or U; the other way round, find R = U/I from current and voltage, and from it the wire length l = R·S/ρ or the cross-section. Units: if ρ is in Ω·mm²/m, then S is in mm² and l in metres; convert mV to volts and mA to amperes. The voltage drop is the voltage across a wire, U = I·R. The answer must make physical sense: a heating coil only 10 mm long would be absurd.
Worked examples
A 24 Ω resistor is to be made from 12 m of nickelin wire. S = ρ·l : R = 0.4 · 12 : 24 = 0.2 mm². With 6 V applied, I = 6 : 24 = 0.25 A.
A nichrome wire l = 10 m, S = 0.5 mm²: R = 1.1 · 10 : 0.5 = 22 Ω. For a current of 0.5 A we need U = I·R = 0.5 · 22 = 11 V.
Class activity
Make your own problem (give substance, length, cross-section and voltage; ask for the current), write its solution in two stages using ρ from the table. Swap and solve with a classmate.
Practice
1
A copper wire (ρ = 0.017 Ω·mm²/m) has l = 50 m, S = 0.85 mm² and 3 V across it. The current (A)?
3
2
A nichrome wire (ρ = 1.1 Ω·mm²/m) 20 m long carries 2 A at 220 V. What is its cross-section in mm²?
0.2
3
A piece of wire of 22 Ω carries 1 A. What is the voltage across it in volts?
22
4
Why is a bird sitting on a bare wire not harmed (consider the part of the wire between its feet)?
The wire section between the feet has a tiny resistance, so U = IR is tiny and almost no current goes through the bird. People must never touch such wires.