How does electrical resistance relate to a cable's length?

How does electrical resistance relate to a cable's length?

• A. Resistance decreases with length
• B. Resistance is independent of length
• C. Resistance changes in proportion to length
• D. Resistance doubles with length

Answer: (C)

Electrical resistance in a cable is influenced by its length due to the fundamental relationship established in Ohm’s Law. Specifically, resistance is directly proportional to the length of the conductor. This means that as the length of the cable increases, the overall resistance also increases. The underlying reason for this relationship is that as electrons travel through a conductor, they encounter resistance caused by collisions with the material's atoms. A longer cable means the electrons have to travel a greater distance, leading to more collisions and thus more resistance. This proportional relationship can be expressed mathematically, where resistance \( R \) is given in the equation \( R = \rho \frac{L}{A} \), where \( \rho \) represents resistivity, \( L \) is the length of the conductor, and \( A \) is the cross-sectional area. This shows that if the length \( L \) increases while the other factors remain constant, the resistance \( R \) will indeed increase in proportion. Hence, the correct understanding is that resistance changes in proportion to the length of the cable.

Electrical resistance in a cable is influenced by its length due to the fundamental relationship established in Ohm’s Law. Specifically, resistance is directly proportional to the length of the conductor. This means that as the length of the cable increases, the overall resistance also increases.

The underlying reason for this relationship is that as electrons travel through a conductor, they encounter resistance caused by collisions with the material's atoms. A longer cable means the electrons have to travel a greater distance, leading to more collisions and thus more resistance. This proportional relationship can be expressed mathematically, where resistance ( R ) is given in the equation ( R = \rho \frac{L}{A} ), where ( \rho ) represents resistivity, ( L ) is the length of the conductor, and ( A ) is the cross-sectional area. This shows that if the length ( L ) increases while the other factors remain constant, the resistance ( R ) will indeed increase in proportion. Hence, the correct understanding is that resistance changes in proportion to the length of the cable.