1. The problem is to apply Kirchhoff's Voltage Law (KVL) to the three loops in the circuit and form the equations for the currents $I_1$, $I_2$, and $I_3$. 2. Kirchhoff's Voltage Law states that the sum of the voltage drops around any closed loop in a circuit is equal to the sum of the voltage sources in that loop. 3. For each loop, write the KVL equation by summing voltage drops ($IR$) and equating to the voltage source. 4. Loop 1 (with current $I_1$): $$10I_1 + 20(I_1 - I_2) + 30I_1 = 1000$$ Explanation: The 20 Ω resistor is shared with loop 2, so voltage drop is $20(I_1 - I_2)$. 5. Loop 2 (with current $I_2$): $$15I_2 + 20(I_2 - I_1) + 40I_2 + 5(I_2 - I_3) = 1000$$ Explanation: The 20 Ω resistor is shared with loop 1 and the 5 Ω resistor is shared with loop 3. 6. Loop 3 (with current $I_3$): $$25I_3 + 5(I_3 - I_2) + 35I_3 = 2000$$ Explanation: The 5 Ω resistor is shared with loop 2. These are the KVL equations for the three loops.