You apply a potential difference of 5.00 V between the ends of a wire that is 2.65 m in length and 0.654 mm in radius. The resulting current through the wire is 17.6 A. What is the resistivity of the wire?
resistance=V/A=rho*Length/Area
I would change .654mm to m
then determine area
solve for Rho
To calculate the resistivity of the wire, we can use the formula:
\[R = \frac{{\rho \cdot L}}{{A}}\]
where:
R is the resistance,
ρ is the resistivity,
L is the length of the wire, and
A is the cross-sectional area of the wire.
First, let's calculate the cross-sectional area of the wire using the radius:
\[A = \pi \cdot r^2\]
Plugging in the values, we get:
\[A = \pi \cdot (0.654 \times 10^{-3})^2\]
Now, let's calculate the resistance:
\[R = \frac{{V}}{{I}}\]
where:
V is the potential difference, and
I is the current.
Plugging in the values, we get:
\[R = \frac{{5.00}}{{17.6}}\]
Now, we can rearrange the formula for resistance to solve for resistivity:
\[\rho = \frac{{R \cdot A}}{{L}}\]
Substituting the values we calculated earlier, we get:
\[\rho = \frac{{\frac{{5.00}}{{17.6}} \cdot \pi \cdot (0.654 \times 10^{-3})^2}}{{2.65}}\]
Solving this equation will give us the resistivity of the wire.
To find the resistivity of the wire, we can use the formula:
Resistance = resistivity * (length / cross-sectional area)
First, let's calculate the cross-sectional area of the wire.
Given:
Length of the wire (l) = 2.65 m
Radius of the wire (r) = 0.654 mm = 0.654 × 10^(-3) m
The formula to calculate the cross-sectional area of a wire is:
Area = π * r^2
Plugging in the values, we get:
Area = π * (0.654 × 10^(-3))^2
We can calculate the area using a calculator, and let's call this value A.
Next, we'll find the resistance using Ohm's Law:
Resistance = Voltage / Current
Given:
Potential Difference (V) = 5.00 V
Current (I) = 17.6 A
Plugging in the values, we get:
Resistance = 5.00 / 17.6
Let's call this value R.
Now we can rearrange the formula for resistance to solve for resistivity:
Resistivity = Resistance * (cross-sectional area / length)
Resistivity = R * (A / l)
Plugging in the values, we get:
Resistivity = R * (A / 2.65)
By calculating this expression using a calculator, we can find the value of the resistivity.