Set the real and imaginary values of the three impedances as well as the magnitude and phase of the two voltage sources.
Step 1. Click on the circuit to assign a current to each independent closed loop.
Step 2. Assuming the current in the shared branch (\( \small{𝑍_2}\)) is pointing to the ground node, once again click on the circuit to indicate the polarities within each loop for each impedance as determined by the assumed direction of loop current for that loop.
Step 3. Apply KVL around each closed loop.
KVL in Loop 1: \( -E_1 + Z_1I_1 + Z_2(I_1-I_2) = 0 \rightarrow \)
KVL in Loop 2: \( -Z_2(I_1-I_2) + Z_3I_2 + E_2 = 0 \rightarrow \)
Step 4. Solve the resulting simultaneous linear equations for the assumed loop currents.
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