Number 10 aluminum wire (radius= 1.3 mm) is commonly used for electrical installations in homes. What is the voltage drop in 20 m of this wire if it carries a current of 10 Amps? The bulk resistivity of aluminum is 2.7*10^-8 Ohm*m
A) 1.3 V
B) 1.9 V
C) 1.0 V
D) 2.5 V
To calculate the voltage drop in a wire, we can use Ohm's Law, which states that voltage drop (V) is equal to current (I) multiplied by resistance (R). In this case, the resistance is the resistance of the aluminum wire.
First, we need to calculate the resistance of the wire. The resistance (R) of a wire can be calculated using the formula:
R = (resistivity * length) / cross-sectional area
Given:
- Radius of the aluminum wire (r) = 1.3 mm = 0.0013 m
- Length of the wire (L) = 20 m
- Current (I) = 10 Amps
- Resistivity of aluminum (ρ) = 2.7 * 10^-8 Ohm*m
First, calculate the cross-sectional area (A) of the wire using the radius:
A = π * r^2
A = 3.14 * (0.0013)^2
A = 5.309 * 10^-6 m^2
Now, plug in the values into the formula for resistance:
R = (ρ * L) / A
R = (2.7 * 10^-8 Ohm*m * 20 m) / (5.309 * 10^-6 m^2)
R = 0.102 Ohms
Now that we have the resistance (R) of the wire, we can calculate the voltage drop (V) using Ohm's Law:
V = I * R
V = 10 Amps * 0.102 Ohms
V = 1.02 V
Therefore, the voltage drop in 20 m of this wire if it carries a current of 10 Amps is approximately 1.02 V.
None of the given answer choices match exactly, but the closest option is C) 1.0 V.
To calculate the voltage drop in the wire, we can use Ohm's Law, which states that the voltage drop (V) across a wire is equal to the product of the current (I) and the resistance (R) of the wire.
First, let's calculate the resistance of the wire using the formula:
R = (resistivity * length) / (cross-sectional area)
The radius of the wire is given as 1.3 mm, which means the diameter is 2 * 1.3 mm = 2.6 mm.
Converting the diameter to meters, we have 2.6 mm = 0.0026 m.
The cross-sectional area of the wire can be calculated as follows:
cross-sectional area = pi * radius^2 = 3.14 * (0.0013 m)^2 ~ 5.309289319e-06 m^2.
Now, substituting the given values into the formula, we get:
R = (2.7 * 10^-8 Ohm*m * 20 m) / (5.309289319e-06 m^2).
Simplifying this expression gives us:
R = 0.0027217662 Ohms.
Now that we know the resistance of the wire, we can calculate the voltage drop using Ohm's Law:
V = I * R.
Substituting the given values, we get:
V = 10 Amps * 0.0027217662 Ohms.
Simplifying this expression gives us:
V ≈ 0.0272176 V.
Therefore, the voltage drop in 20 m of this wire is approximately 0.0272176 V, which is close to 0.03 V.
Therefore, the correct answer is not provided.