(Solved): Consider the configuration of current-carrying wires shown below. Two semi- ...

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Consider the configuration of current-carrying wires shown below. Two semi-infinite wires carry equal currents $$I_1$$ and $$I_2$$, each with magnitude $$I_0$$ as shown. These wires meet at Point A, where their currents combine and split to form currents $$I_3$$ and $$I_4$$, which run down two semi-circular arcs of radius $$a$$. These currents combine again at Point B to form $$I_5=2I_0$$, which is carried away in a third semi-infinite wire along the $$?y$$ axis. On the left-hand arc, the upper and lower quarter circles of wire each have resistance $$R$$. On the right-hand arc, the upper quarter circle has resistance $$2R$$ and the lower quarter circle has resistance $$R$$. Thus, this system can be viewed as the following equivalent circuit: (a) What is the equivalent resistance $$R_{AB}$$ measured between Points A and B? (b) What is the potential difference between Points A and $$\mathrm{B},?V=V_A?V_B$$ ? (c) What are the currents $$I_3$$ and $$I_4$$ ?