Harold Hall



Workshop Data

Do note that in practice components will be sized in Milli Henries and Micro Farads. See my comments on my DC pages for clarification, Farads and Henries.


In these cases the current will be out of phase with the supply voltage by 90°, leading in the case of capacitive reactance (Sk2B) and lagging when inductive (Sk2C).


In practice, pure inductance or pure capacitance rarely occur and the effect of a resistive element must be taken into account. As the current due to the resistive element will be in phase, resistance and reactance cannot be added to arrive at a value for the impedance, Z. The formula for an inductive circuit being,


     Z  =  √SR² + Xl²

and for a capacitive circuit.


     Z  =  √SR² + Xc²


Because the currents due to inductance and capacitance lag and lead by 90°, that is with 180° between them, their total reactance is not the sum but their difference. The formula therefor becomes for a circuit containing both inductance and capacitance.


      Z  =   √SR² + (Xl - Xc)²


Having arrived at a value for Z then the current taken can easily be calculated using the simple formula.



      I  =  ———



Power in an AC circuit

Here we come to the vital point mentioned earlier! From this one may assume that having arrived at a value for the current (I) the power consumed would just be the product of V and I as is the case in a DC situation. This is not the case and is due to the fact that the voltage and current waveforms are out of phase. The amount is though not fixed as it is dependent on the relative values of the resistive and inductive/capacitive elements.

Beyond purely resistive loads the formula required will still be very similar but the term resistance (R) is replaced by impedance (Z), typically.



          I  =  ———



Impedance, Z, is more complex as it is frequently not a value for a single characteristic but a combination of resistance, capacitance and or inductance. This is necessary as they frequently occur together in a single component. Typically, the windings of a coil will have a resistance and inductance.


As mentioned above, resistance performs identically in both AC and DC circuits. However, unlike capacitance and inductance in a DC circuit where a steady state condition is arrived at some time after being energised, the continually changing voltage of an AC supply means that the charge on a capacitor or the field strength created in a coil is continually changing. This makes arriving at a value for Z more complex, especially as the effects of inductive and capacitive elements in a circuit are also frequency dependent.


The term for the characteristic that determines the flow of current through a pure inductor or capacitor is called "reactance" and is known by the letter "X". The value for this can be calculated using the following formula.


Inductive reactance   Xl = 2 P f L ohms


Where  P equals 3.14

      f equals the frequency in Hertz

      L equals the inductance in Henries


Similarly                      1

Capacitive reactance  Xc = ————————— ohms

                           2 P f C


Where C equals the capacitance in Farads.

Assuming pure inductance or capacitance the resulting current would be.


           V                    V

    I  =  ———     or     I  =  ———

           Xl                   Xc