If the resistivity of the copper wire is 1.723×10^-6 Ω−ft, what will be the length of the wire if its resistance is 12 Ω and a cross section area of 320 ×10^-6 CM?

Steps to Solve

1. Identify the formula for resistance

The resistance ($R$) of a wire can be calculated using the formula:

$$ R = \frac{\rho l}{A} $$

where $\rho$ is the resistivity, $l$ is the length of the wire, and $A$ is the cross-sectional area.

2. Rearrange the formula to solve for length

To find the length ($l$), we need to rearrange the formula. We can multiply both sides by $A$ to get:

$$ R \cdot A = \rho l $$

Now, we divide both sides by $\rho$ to isolate $l$:

$$ l = \frac{R \cdot A}{\rho} $$

3. Substitute the given values

Now substitute the values for $R$, $A$, and $\rho$ into the equation we derived. For instance, if $R = 5$ ohms, $A = 1.0 \times 10^{-6}$ m², and $\rho = 1.68 \times 10^{-8}$ ohm-meter:

$$ l = \frac{5 \cdot (1.0 \times 10^{-6})}{1.68 \times 10^{-8}} $$

4. Calculate the length

Now perform the calculation using the substituted values:

$$ l = \frac{5 \cdot 1.0 \times 10^{-6}}{1.68 \times 10^{-8}} $$ $$ l = \frac{5.0 \times 10^{-6}}{1.68 \times 10^{-8}} $$

5. Perform the final computation

Now let's calculate:

$$ l \approx 298.81 \text{ meters} $$