Question
Which of the following wires would have the LEAST resistance? (Assume that the wires have the same cross-sectional area.)
a
an aluminum wire 10 cm in length
b
a copper wire 5 cm in length
c
an aluminum wire 5 cm in length
d
a copper wire 10 cm in length
Question 9 (1 point)
Which of the following wires would have the GREATEST resistance?
a
an aluminum wire 10 cm in length and 5 cm in diameter
b
an aluminum wire 5 cm in length and 5 cm in diameter
c
an aluminum wire 5 cm in length and 3 cm in diameter
d
an aluminum wire 10 cm in length and 3 cm in diameter
a
an aluminum wire 10 cm in length
b
a copper wire 5 cm in length
c
an aluminum wire 5 cm in length
d
a copper wire 10 cm in length
Question 9 (1 point)
Which of the following wires would have the GREATEST resistance?
a
an aluminum wire 10 cm in length and 5 cm in diameter
b
an aluminum wire 5 cm in length and 5 cm in diameter
c
an aluminum wire 5 cm in length and 3 cm in diameter
d
an aluminum wire 10 cm in length and 3 cm in diameter
Answers
GPT-4o mini
To determine the resistance of the wires, we can use the formula for resistance:
\[ R = \rho \frac{L}{A} \]
where:
- \( R \) is resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the wire, and
- \( A \) is the cross-sectional area of the wire.
Given that all wires have the same cross-sectional area in the first question, we can simplify our comparisons by focusing on the resistivity of the materials (aluminum vs. copper) and the length of the wires.
### Question 8: Which wire has the least resistance?
1. **Aluminum wire (10 cm):** Longer length means greater resistance.
2. **Copper wire (5 cm):** Copper has lower resistivity than aluminum, and shorter length means lower resistance than aluminum wire of the same length.
3. **Aluminum wire (5 cm):** Shorter length but still higher resistivity than copper.
4. **Copper wire (10 cm):** Longer length increases resistance, but still lower than aluminum's resistance.
In summary:
- The copper wire (5 cm in length) would have the least resistance due to its lower resistivity and shorter length.
**Answer: b) a copper wire 5 cm in length.**
### Question 9: Which wire has the greatest resistance?
For this question, we must consider both length and diameter (which affects the cross-sectional area). The cross-sectional area \( A \) for a wire can be calculated from its diameter (the area increases with the square of the diameter).
1. **Aluminum wire (10 cm, 5 cm diameter):** Longer length (10 cm) yields higher resistance, but larger diameter reduces resistance.
2. **Aluminum wire (5 cm, 5 cm diameter):** Shortest length here offers the lowest resistance for this diameter.
3. **Aluminum wire (5 cm, 3 cm diameter):** Shortest length, but smaller diameter than the previous option, meaning resistance will be higher.
4. **Aluminum wire (10 cm, 3 cm diameter):** This wire has the longest length (10 cm) and the smallest diameter (3 cm), leading to the highest resistance.
In summary:
- The aluminum wire (10 cm, 3 cm diameter) has the greatest resistance because it has the longest length and the smallest diameter, which increases its resistance.
**Answer: d) an aluminum wire 10 cm in length and 3 cm in diameter.**
\[ R = \rho \frac{L}{A} \]
where:
- \( R \) is resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the wire, and
- \( A \) is the cross-sectional area of the wire.
Given that all wires have the same cross-sectional area in the first question, we can simplify our comparisons by focusing on the resistivity of the materials (aluminum vs. copper) and the length of the wires.
### Question 8: Which wire has the least resistance?
1. **Aluminum wire (10 cm):** Longer length means greater resistance.
2. **Copper wire (5 cm):** Copper has lower resistivity than aluminum, and shorter length means lower resistance than aluminum wire of the same length.
3. **Aluminum wire (5 cm):** Shorter length but still higher resistivity than copper.
4. **Copper wire (10 cm):** Longer length increases resistance, but still lower than aluminum's resistance.
In summary:
- The copper wire (5 cm in length) would have the least resistance due to its lower resistivity and shorter length.
**Answer: b) a copper wire 5 cm in length.**
### Question 9: Which wire has the greatest resistance?
For this question, we must consider both length and diameter (which affects the cross-sectional area). The cross-sectional area \( A \) for a wire can be calculated from its diameter (the area increases with the square of the diameter).
1. **Aluminum wire (10 cm, 5 cm diameter):** Longer length (10 cm) yields higher resistance, but larger diameter reduces resistance.
2. **Aluminum wire (5 cm, 5 cm diameter):** Shortest length here offers the lowest resistance for this diameter.
3. **Aluminum wire (5 cm, 3 cm diameter):** Shortest length, but smaller diameter than the previous option, meaning resistance will be higher.
4. **Aluminum wire (10 cm, 3 cm diameter):** This wire has the longest length (10 cm) and the smallest diameter (3 cm), leading to the highest resistance.
In summary:
- The aluminum wire (10 cm, 3 cm diameter) has the greatest resistance because it has the longest length and the smallest diameter, which increases its resistance.
**Answer: d) an aluminum wire 10 cm in length and 3 cm in diameter.**