(Solved): 2) Use Mesh (Loop) analysis to analyze the circuit shown below: k) Check your answers by writing t ...

2) Use Mesh (Loop) analysis to analyze the circuit shown below: k) Check your answers by writing the complex number equations for the given original circuit schematic as requested in the following: Write a complex KVL around the left loop. Write a complex KVL around the right loop. Write a complex KCL at the top node. The complex number phasor voltage values for the voltage sources are shown on the schematic. The complex number impedances for the circuit components are also shown on the schematic. Notes: On the schematic impedance \( Z R \# \) means impedance \( Z_{R \#} \) The inductor's complex impedance \( Z_{\mathrm{L}}=\mathbf{6} \mathrm{k} \Omega<90^{\circ} \) and capacitor's complex impedance \( Z_{\mathrm{c}}=12 \mathrm{k} \Omega<-90^{\circ} \) Use Mesh (Loop) Analysis in this problem: a) Consider the clockwise complex phasor Mesh Current in the left side mesh (loop) to be \( \mathbf{I}_{A} \) and consider the clockwise complex phasor Mesh Current in the right side mesh (loop) to be \( \mathbf{I}_{B} \) in the circuit drawn above. Redraw the circuit with the Mesh Currents \( I_{A} \) and \( I_{B} \) labeled on the diagram Your drawing should show the Mesh Currents \( I_{A} \) and \( I_{B} \), but the following variable names should be omitted from your drawing: \( V_{R 1}, V_{L}, V_{R 3}, I_{R 3}, V_{R 2} \), and \( V_{C} \) b) Write the complex KVL (Kirchhoff's Voltage Law) Mesh equations for the left mesh (loop) and for the right mesh (loop). Also substitute in the complex number element voltage equations in the form: \( V=I \cdot Z \) c) Solve the complex number KVL Mesh equations for complex phasor Mesh Currents \( I_{A} \) and \( I_{B} \) d) Find the complex phasor currents through and voltages across each of the elements in the circuit