I've often struggled to get to grips with a.c. circuit calculations involving resistance, capacitance and inductance. There is quite a lot of tricky mathematical jargon here - vector sums, phasors, polar notation, angular velocity etc etc.
I decided to tackle this head on today and improve my understanding! First of all I learnt about the reactance of inductors and capacitors, which is given units of Ohms. If inductors and capacitors are 'pure reactance, and do not dissipate energy', how can they have a property measured in Ohms? Well I deal with this in my mind by remembering that current does flow back and forth through the inductors and capacitors, and energy flows into and out of these passive components. So reactance is a convenient way of dealing with working out what the magnitude of this current is. It does not mean that the inductor or capacity has some kind of resistive quality.
The next thing I learnt is that the resistance of a resistor can be treated as a 'real' quantity, and the reactance of an inductor or capacitor can be thought of as an 'imaginary' quantity. You can add real quantities, and you can add imaginary quantities together, but you cannot add a real quantity to an imaginary one.
The final thing I learnt is that resistors, capacitors and inductors can all be thought of as having an impedance, and an impedance has a real and imaginary part. For resistors the imaginary part is zero, and for capacitors and inductors the real part is zero. Inductors have a positive imaginary value and capacitors have a negative imaginary value.
Whilst all of this was fresh in my mind I quickly put together the following web page concerned with an electrical circuit with impedances connected in series.
I hope that my understanding is correct , and thank you once again for reading!