Given two impedances Z1 and Z2 connected in parallel, what is their impedance expressed in real and imaginary parts?
For impedances in parallel, the formula is:
Expressing each impedance Z1 and Z2 individually as:
Here is the online calculator tool:
(Note: Polar notation using angle symbol ∠Ð to be added later)
(Remember that the imaginary part is positive for inductive reactance, and negative for capacitive reactance)
Formula Derivation
We can now derive an expression for the combined impedance Z:
Re-arranging the denominator gives:
Now, multiplying above and below by:
Gives Us:
Now, recognising that:
We can expand to give:
So, the solution is:
Impedances in Parallel Excel Spreadsheet