Question

1. which factor would increase resistance of a wire? thicker wires cooler wires thinner wires shorter wires

Explanation:

Step1: Recall the formula for resistance

The resistance \( R \) of a wire is given by the formula \( R=
ho\frac{l}{A} \), where \(
ho \) is the resistivity (a property of the material), \( l \) is the length of the wire, and \( A \) is the cross - sectional area of the wire.

Step2: Analyze the effect of each option

• Thicker wires: A thicker wire has a larger cross - sectional area \( A \). From \( R =

ho\frac{l}{A} \), when \( A \) increases (assuming \(
ho \) and \( l \) are constant), \( R \) decreases.

• Cooler wires: For most materials (except some semiconductors in certain cases), as the temperature decreases (cooler wires), the resistivity \(

ho \) decreases (for metals, the relationship \(
ho=
ho_0(1 + \alpha\Delta T) \) where \( \alpha>0 \) for metals). So, \( R=
ho\frac{l}{A} \) will decrease if \(
ho \) decreases (assuming \( l \) and \( A \) are constant).

• Thinner wires: A thinner wire has a smaller cross - sectional area \( A \). Using \( R=

ho\frac{l}{A} \), when \( A \) decreases (assuming \(
ho \) and \( l \) are constant), \( R \) increases.

• Shorter wires: A shorter wire has a smaller length \( l \). From \( R=

ho\frac{l}{A} \), when \( l \) decreases (assuming \(
ho \) and \( A \) are constant), \( R \) decreases.

Answer:

thinner wires