Calculate the resistance per unit length of a nichrome wire, which has a radius of 0.436 mm. The resistivity of nichrome is 1.5×10−6 Ω·m.
Answer in units of Ω/m
If a potential difference of 20 V is maintained across a 3.7 m length of the nichrome wire, what is the current in the wire?
Answer in units of A
3.579 A
To calculate the resistance per unit length of the nichrome wire, we can use the formula:
Resistance per unit length (R') = (Resistivity * Length) / Area
Here, the resistivity of nichrome is given as 1.5x10^-6 Ω·m and the radius of the wire is 0.436 mm (which we need to convert to meters).
First, let's convert the radius from millimeters to meters:
Radius (r) = 0.436 mm = 0.436 * 10^-3 m = 4.36x10^-4 m
Next, we can calculate the area of the wire using the radius:
Area (A) = π * r^2
A = 3.14 * (4.36x10^-4 m)^2
Now, we can use the formula to calculate the resistance per unit length:
R' = (1.5x10^-6 Ω·m * 1 m) / (3.14 * (4.36x10^-4 m)^2)
Performing the calculation:
R' = (1.5x10^-6) / (3.14 * (4.36x10^-4)^2)
Now, let's calculate the resistance per unit length.
To find the resistance per unit length, divide the resistivity by the area squared, and multiply by 1 meter:
R' = (1.5x10^-6) / (3.14 * (4.36x10^-4)^2) * 1
Multiply the numerator and denominator to simplify:
R' = 1.5x10^-6 / (3.14 * (4.36x10^-4)^2)
Now, we can calculate the current through the wire.
We are given a potential difference of 20 V and a length of 3.7 m. To find the current, we will use Ohm's Law:
Current (I) = Potential difference (V) / Resistance (R)
We can use the resistance per unit length (R') calculated earlier to find the total resistance (R):
Resistance (R) = Resistance per unit length (R') * Length (L)
R = R' * L
Substituting the given values into the equation:
R = R' * 3.7 m
Finally, we can calculate the current (I) using Ohm's Law:
I = V / R
Substituting the given values into the equation:
I = 20 V / R
Let's calculate the resistance per unit length (R') and the current (I) using the given values.