Physics - Current Electricity Question with Solution | TestHub

The bare wire in parallel with the $5\Omega$ resistor shorts it (it carries no current), and the $4\Omega$-triangle hangs from a single node, so $I_3=I_4=0$.

The main loop carries $10\mathrm{A}$. The $6\Omega$ pair carries $6\mathrm{A}$ (drop $=36\mathrm{V}$), so the remaining $4\mathrm{A}$ flows through $R$: $R=36/4=9\Omega$ - option (A) correct.

Each $3\Omega$ resistor carries $10/2=5\mathrm{A}$, so $I_1=5\mathrm{A}$ - option (D) correct.

Around the main loop: $\epsilon =10\times 2+36+6+10\times 4+10\times 1.5=117\mathrm{V}$ - option (C) correct, (B) false.

Answers: (A), (C), (D).