Le tableau suivant montre les données de trois fils composés du même conducteur dans lequel circule le même courant. Classez les fils selon un ordre croissant: a. la résistance ; b... Le tableau suivant montre les données de trois fils composés du même conducteur dans lequel circule le même courant. Classez les fils selon un ordre croissant: a. la résistance ; b. la différence de potentiel à leurs bornes. Fil Diamètre Longueur 1 1D 1L 2 2D 2L 3 D÷2 1L Read more

Steps to Solve

1. Calculate the resistance of each wire

Resistance $R$ is given by the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area. Since the resistivity $\rho$ is the same for all wires, we can compare the resistances based on the ratio $\frac{L}{A}$. The area $A$ can be expressed in terms of the diameter $d$ as $A = \pi (\frac{d}{2})^2 = \frac{\pi d^2}{4}$. Thus, $R \propto \frac{L}{d^2}$.

2. Wire 1: Length $L$, Diameter $d$

$R_1 \propto \frac{L}{d^2}$

3. Wire 2: Length $2L$, Diameter $d/2$

$R_2 \propto \frac{2L}{(d/2)^2} = \frac{2L}{d^2/4} = \frac{8L}{d^2}$

4. Wire 3: Length $L/3$, Diameter $3d$

$R_3 \propto \frac{L/3}{(3d)^2} = \frac{L/3}{9d^2} = \frac{L}{27d^2}$

5. Compare the resistances

Comparing $R_1$, $R_2$, and $R_3$, we have: $R_1 \propto \frac{L}{d^2}$ $R_2 \propto \frac{8L}{d^2}$ $R_3 \propto \frac{L}{27d^2}$

Clearly, $R_3 < R_1 < R_2$.

6. Calculate the potential difference across each wire

Potential difference $V$ (voltage) is given by Ohm's law: $V = IR$. Since the current $I$ is the same for all wires, we can compare the potential differences based on their resistances.

7. Potential difference ranking

Since $R_3 < R_1 < R_2$ and $V = IR$, we have $V_3 < V_1 < V_2$.

8. Final Answer

The wires, in order of increasing resistance, are 3, 1, 2. The wires, in order of increasing potential drop, are 3, 1, 2.