1. **State the problem:** Apply Kirchhoff's Voltage Law (KVL) to each of the three loops in the circuit to form equations involving currents $I_1$, $I_2$, and $I_3$. 2. **Recall KVL:** The sum of voltage drops around any closed loop equals the sum of voltage sources in that loop. 3. **Define currents and resistors:** - Left loop: voltage source $1000$ V, resistors $10\ \Omega$, $30\ \Omega$, and shared resistor $20\ \Omega$ with middle loop. - Middle loop: voltage source $1000$ V, resistors $15\ \Omega$, $40\ \Omega$, and shared resistors $20\ \Omega$ (left) and $5\ \Omega$ (right). - Right loop: voltage source $2000$ V, resistors $25\ \Omega$, $35\ \Omega$, and shared resistor $5\ \Omega$ with middle loop. 4. **Write KVL for each loop:** **Left loop:** $$1000 - 10I_1 - 20(I_1 - I_2) - 30I_1 = 0$$ **Middle loop:** $$1000 - 15I_2 - 5(I_2 - I_3) - 40I_2 - 20(I_2 - I_1) = 0$$ **Right loop:** $$2000 - 25I_3 - 35I_3 - 5(I_3 - I_2) = 0$$ These are the KVL equations for the three loops.