# Complex impedance calculation for resistors and coil

I have this circuit and I need to calculate the total complex impedance.

Note: the $$\r\$$ is internal resistance of the coil so how can we calculate the complex impedance?

The coil and the resistance $$\R\$$ are in parallel.

• If you want a numerical answer you need to provide the operating frequency of the circuit. Do you understand complex numbers to any degree? Commented Mar 10, 2021 at 11:12
• @Andyaka yes the frequency of the circuit is 50 Hz , i want to know how can i calculate the complex impedance with this internal resistance r of the coil , Commented Mar 10, 2021 at 11:24

$$\underline{\text{Z}}_{\space\text{in}}=\text{R}\text{||}\left(\text{r}+\text{j}\omega\text{L}\right)=\frac{\text{R}\left(\text{r}+\text{j}\omega\text{L}\right)}{\text{R}+\text{r}+\text{j}\omega\text{L}}\tag1$$
$$\underline{\text{Z}}_{\space\text{in}}=\frac{220\left(100+\text{j}\cdot2\pi\cdot50\cdot550\cdot10^{-3}\right)}{220+100+\text{j}\cdot2\pi\cdot50\cdot550\cdot10^{-3}}=$$ $$220-\frac{619520}{4096+121 \pi ^2}+\frac{106480 \pi \text{j}}{4096+121 \pi ^2}\approx102.893+63.233\text{j}\tag2$$