Question 1.17: A coil consists of an 8 m length of annealed copper wire hav......

Electronic Circuits Fundamentals and Applications
Circuit Design Know It All [1385950]
Aircraft Engineering Principles
Electronic Circuits Fundamentals and Applications [1001472]

A coil consists of an 8 m length of annealed copper wire having a cross-sectional area of 1 mm². Determine the resistance of the coil.

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

We will use the formula, R = ρl / A.

The value of , for annealed copper given in Table 1.5 is 1.724 × 10 $^{-8}$ Ωm. The length of the wire is 4 m while the area is 1 mm² or 1 × 10 $^{-6}$ m² (note that it is important to be consistent in using units of metres for length and square metres for area).

Hence the resistance of the coil will be given by:

R  =  \frac{1.724  \times  10^{-8}  \times  8}{1  \times  10^{-6}}  =  13.724  \times  10^{(-8+6)}

Thus R = 13.792 × 10 $^{-2}$ or 0.13792 Ω

Table 1.5 Properties of some common metals
Metal	Resistivity (at 20°C) (Ωm)	Relative conductivity (copper = 1)	Temperature coefficient of resistance (per °C)
Silver	1.626 × 10 $^{-8}$	1.06	0.0041
Copper (annealed)	1.724 × 10 $^{-8}$	1.00	0.0039
Copper (hard drawn)	1.777 × 10 $^{-8}$	0.97	0.0039
Aluminium	2.803 × 10 $^{-8}$	0.61	0.0040
Mild steel	1.38 × 10 $^{-7}$	0.12	0.0045
Lead	2.14 × 10 $^{-7}$	0.08	0.0040
Nickel	8.0 × 10 $^{-8}$	0.22	0.0062