Chapter 12, Problem 10P

To determine

Create a Table of relative resistance of the metals given in the Table 12.1 in the textbook.

Answer to Problem 10P

The table has been created as below.

Metal	Resistance $\left(\Omega \right)$	Relative Resistance to Copper
Aluminum	17.01	1.64
Brass	66.8	6.44
Copper	10.37	1
Gold	14.7	1.42
Iron	59.9	5.78
Lead	132	12.73
Nickel	50.8	4.9
Platinum	63.8	6.15
Silver	9.8	0.95
Tin	70	6.75
Tungsten	33.2	3.2
Zinc	35.58	3.43

Explanation of Solution

Given data:

Refer to Table 12.1 in the textbook, which shows the Electrical Resistance for 1 ft long Wire, made of Various Metals Having a Diameter of 1 mil at $20°\text{C}$.

The relative resistance of the wire of “1 ft long and 1 mil diameter of aluminum wire” to “1 ft long and 1 mil diameter of aluminum” is calculated as,

$\begin{array}{l}=\frac{17.01\Omega }{10.37\Omega }\\ =1.64\end{array}$

Formula used:

Formula to calculate the relative resistance of the material is given by,

$R_{\text{R}}=\frac{R_{\text{metal}}}{R_{\text{copper}}}$ (1)

Heer,

$R_{\text{metal}}$ is the resistance of the metal.

$R_{\text{copper}}$ is the resistance of the copper.

Resistance of the copper $\left(R_{\text{copper}}\right)$ is standard scale to measure the relative resistance of the any metal.

Calculation:

Refer to Table 12.1 in the textbook, it shows the relative resistance of 1 ft long wires with 1 mil diameter size..

Substitute 17.01 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ to find relative resistance of aluminum,

$\begin{array}{c}{R}_{\text{R}}=\frac{17.01\text{Ω}}{10.37\text{Ω}}\\ =1.64\end{array}$

Therefore, the relative resistance of the aluminum is $1.64$.

Substitute 66.8 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of brass metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{66.8\text{Ω}}{10.37\text{Ω}}\\ =6.44\end{array}$

Therefore, the relative resistance of the brass is $6.44$.

Substitute 10.37 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of copper metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{10.37\text{Ω}}{10.37\text{Ω}}\\ =1.00\end{array}$

Therefore, the relative resistance of the copper metal is 1.00.

Substitute 14.7 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of gold metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{14.7\text{Ω}}{10.37\text{Ω}}\\ =1.42\end{array}$

Therefore, the relative resistance of the gold is 1.42.

Substitute 59.9 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of iron metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{59.9\text{Ω}}{10.37\text{Ω}}\\ =5.78\end{array}$

Therefore, the relative resistance of the iron is 5.78.

Substitute 132 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of lead metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{132\text{Ω}}{10.37\text{Ω}}\\ =12.73\end{array}$

Therefore, the relative resistance of the lead is 12.73.

Substitute 50.8 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of nickel metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{50.8\text{Ω}}{10.37\text{Ω}}\\ =4.90\end{array}$

Therefore, the relative resistance of the nickel is 4.90.

Substitute 63.8 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of platinum metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{63.8\text{Ω}}{10.37\text{Ω}}\\ =6.15\end{array}$

Therefore, the relative resistance of the platinum is 6.15.

Substitute 9.8 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of silver metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{9.8\text{Ω}}{10.37\text{Ω}}\\ =0.95\end{array}$

Therefore, the relative resistance of the silver is 0.95.

Substitute 70 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of tin metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{70\text{Ω}}{10.37\text{Ω}}\\ =6.75\end{array}$

Substitute 33.2 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of tungsten metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{33.2\text{Ω}}{10.37\text{Ω}}\\ =3.20\end{array}$

Therefore, the relative resistance of the tungsten is 3.20.

Substitute 35.58 for $R_{\text{metal}}$ and $10.37\text{Ω}$ for $R_{\text{copper}}$ in equation (1) to find relative resistance of Zinc metal,

$\begin{array}{c}{R}_{\text{R}}=\frac{35.58\text{Ω}}{10.37\text{Ω}}\\ =3.43\end{array}$

Therefore, the relative resistance of the Zinc is 3.43.

Conclusion:

Hence the Table for relative resistance of the metals is has been created.