A wire of length, I, and cross-sectional area, A, has a resistance, R. Another wire of the same material is three times as long and with the same cross-sectional area. Compare their resistances.

The resistance $R$ of a wire is given by the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length, and $A$ is the cross-sectional area.

For the first wire, let its resistance be $R_1$, length $L_1 = L$, and cross-sectional area $A_1 = A$.
So, the resistance of the first wire is:

For the second wire, it is made of the same material (so resistivity $\rho$ is the same), its length $L_2 = 3L$, and its cross-sectional area $A_2 = A$.
So, the resistance of the second wire is:

We can rewrite the expression for $R_2$ by factoring out the constant 3:

Since $R_1 = \rho \frac{L}{A}$, we can substitute $R_1$ into the equation for $R_2$:

The second wire has three times the resistance of the first wire.