Complex Circuit Analysis

Question:

Using complex circuit analysis, solve the circuit below to find the total network impedance and supply current. Before starting the calculations identify and explain the relevant theory and strategies that you will be using ensuring that you demonstrate how you have determined the correctness of your answers.

Answer:

Steps to answer this question:

Step 1: Split the circuit into 4 branches.

Step 2: 3 parallel branches and 1 series branch.

Step 3: Calculate Admittance in the 1st, 2nd and 3rd branch.

Step 4: Calculate total parallel Admittance through the following:

Step 5: Calculate parallel Impedance through the following:

Step 6: Calculate branch 4 Impedance.

Step 7: Calculate total Impedance for the circuit using the following formula:

Step 8: Find the current through the following formula:

Step 9: Check current value by totaling individual branch currents.

A diagram of the circuit is shown below and the branches have been labelled 1 to 4.

Branch 1 capacitor:

Branch 1 Impedance:

Branch 1 Admittance:

Branch 2 Inductor:

Branch 2 Impedance:

Branch 2 Admittance:

Branch 3 Impedance:

Branch 3 Admittance:

Branch 4 Inductor:

Branch 4 Impedance:

Total Parallel Admittance:

Total Parallel Impedance:

Total Circuit Impedance:

Supply Current:

Voltage Across Parallel Branch and a modified circuit diagram simplifying the circuit for analysis:

Branch 1 Current:

Branch 2 Current:

Branch 3 Current:

As the currents match we can be sure the solution is correct.