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
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
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
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.
I = ——— or I = ———