5.5. Work and power of alternating current
Elementary
work of an external alternating EMF equals
product of instant values of EMF
current
and
elementary time
Instantaneous power of an alternating current is
For an electric circuit section total instantaneous power is
where
is voltage drop across the circuit
section.
Form
of energy
release at alternating current flow depends on the circuit
components
and
Following energy
transformations are possible:
a) energy of alternating current transforms into Joule heat which an ohmic resistance releases
Is voltage drop across the ohmic resistance);
b) energy of alternating current transforms in energy of the magnetic field which creates in the inductance coil; instantaneous power of an alternating current in the case is
Instantaneous
power
can be negative
when
the magnetic
field decreases; hence, the electric circuit
returns energy
to the external alternating EMF;
c)
energy
of alternating current transforms
in energy
of the electric field which creates in the capacitor; instantaneous
power of an alternating current in the case is
Instantaneous
power
can be negative too
it means that the
capacitor discharges.
Total instantaneous power of the external alternating EMF
where
and
are
voltage drops across the circuit resistance, capacitance,
and inductance.
Mean power of alternating current
(2.93)
Mean power of alternating current differs from zero only for ohmic resistance (work of alternating current turns into Joule heat). Capacitance and inductance are energetically neutral.
equation (2.93) can be rewritten:
(2.95)
It is obvious that the same heat power is released by direct current and EMF which values equal
(2.96)
(2.97)
The
values (2.96) and (2.97) for alternating
current are cold effective
or for voltage –
rms voltage. Hence, effective values of
alternating
current are
times less than their amplitude values.
Ammeters and voltmeters measure only effective values of alternating current. Their amplitude values are 1.4 times larger; it has to be taken into account at design of electric insulators for safe working conditions.
Equations (2.96) and (2.97) show that equations deduced for amplitude values are true for effective ones; for example, equation (2.58) can be rewritten as
General
form of the Ohm law is
Hence, equation
(2.95)
of mean power of
alternating current can be rewritten
as
(2.98)
Taking into account equation for phase shift
(2.99)
Substitute
for
in equation (2.98) and get
(2.100)
or using effective
values
and
we get
(2.101)
Magnitude
in
equation (2.101) is cold power factor or
cos phi.
Hence,
mean power of
alternating current depends on the phase
shift. It means that mean power of
alternating current in an electric circuit
with ohmic
resistance,
capacitance, and inductance
is less
than mean power of an
electric circuit with ohmic
resistance but
without capacitance
and inductance
.
The
mean powers are equal only in case of resonance
.
If
we decrease capacitance
phase shift
decreases and power factor
increases.
As a result, we see increase
of the lamp
brightness. The alternating
EMF effective value
remains the same while the electric
circuit mean
power increases.
Therefore, we can increase power factor of any circuit of alternating current by reactivity insertion