## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

We can rank the currents in order from largest to smallest: $I_1 = I_4 \gt I_2 = I_3$
Since all the wires have the same diameter and they are made of the same material, the resistivity of each wire is the same. Since the currents $I_2$ and $I_3$ move through wires of the same total length, the resistance is the same. Since the potential difference is the same across both branches of the middle section, $I_2 = I_3$ $I_1$ and $I_4$ are equal to the total current flowing through the wire since there is only one path at these sections. Therefore, $I_1 = I_4$. $I_2$ and $I_3$ are both equal to half the total current since there are two equal paths at this section. We can rank the currents in order from largest to smallest: $I_1 = I_4 \gt I_2 = I_3$