What will happen to the resistance of a wire if its length is multiplied by 3?
2 Answers
To understand what happens to the resistance of a wire if its length is multiplied by 3, we need to consider the formula for resistance: \( R = \rho \frac{L}{A} \), where \( R \) is the resistance, \( \rho \) is the resistivity of the material, \( L \) is the length of the wire, and \( A \) is the cross-sectional area.
If you multiply the length \( L \) by 3, while keeping the resistivity \( \rho \) and cross-sectional area \( A \) constant, the new resistance \( R' \) can be calculated as:
\[ R' = \rho \frac{3L}{A} = 3 \left( \rho \frac{L}{A} \right) = 3R \]
So, the resistance of the wire will also be multiplied by 3.
If you multiply the length \( L \) by 3, while keeping the resistivity \( \rho \) and cross-sectional area \( A \) constant, the new resistance \( R' \) can be calculated as:
\[ R' = \rho \frac{3L}{A} = 3 \left( \rho \frac{L}{A} \right) = 3R \]
So, the resistance of the wire will also be multiplied by 3.