I said that [itex]A\ell=A_{\textrm{new}}\ell\left(1+\frac{x}{100}\right)\implies A_{\textrm{new}}=\frac{A}{1+\frac{x}{100}}[/itex]. Also, we know that [itex]R\propto\frac{\ell}{A}.[/itex]. Therefore,A cylindrical wire of length [itex]\ell[/itex] and cross-sectional area [itex]\textrm{A}[/itex] has a fixed volume [itex]\textrm{V}[/itex]. If [itex]\ell[/itex] is increased by [itex] +x [/itex] percent and the volume and resistivity stay the same, by what percentage (in terms of [itex]x[/itex]) will the resistance change?
The quadratic term in the resistance equation refers to the term that is squared. In the case of the resistance equation, the quadratic term is the term that includes the velocity squared.
Expanding the quadratic term in the resistance equation allows for a more accurate calculation of resistance. It takes into account the non-linear relationship between velocity and resistance, which is necessary for more precise calculations.
No, the quadratic term should not be ignored in the resistance equation. Ignoring it will result in a less accurate calculation of resistance.
To expand the quadratic term in the resistance equation, you need to square the term that includes the velocity. Then, you can combine like terms and simplify the equation as needed.
The purpose of expanding the quadratic term in the resistance equation is to account for the non-linear relationship between velocity and resistance. This allows for more accurate calculations and predictions in scientific experiments and engineering designs.