In the context of electrical engineering, A.C. fundamentals refer to the fundamental concepts and principles associated with alternating current (A.C.) electrical systems. One important concept within A.C. fundamentals is instantaneous power.
Instantaneous Power in A.C. Circuits:
Instantaneous power is the power (rate of energy transfer) at any specific instant in an alternating current (A.C.) circuit. In A.C. circuits, voltage and current values continuously vary sinusoidally with time. As a result, the power also varies with time, and its value at any given moment is known as instantaneous power.
Mathematically, instantaneous power (P_inst) in an A.C. circuit can be calculated using the following formula:
=
(
)
×
(
)
P
inst
=v(t)×i(t)
Where:
P
inst
= Instantaneous power at time
t
(
)
v(t) = Instantaneous voltage at time
t
(
)
i(t) = Instantaneous current at time
t
For sinusoidal waveforms, such as those commonly encountered in A.C. circuits, the instantaneous power expression can be further refined. If
(
)
v(t) and
(
)
i(t) are expressed as sinusoidal functions of time:
(
)
=
⋅
cos
(
+
)
v(t)=V
m
⋅cos(ωt+ϕ
v
)
(
)
=
⋅
cos
(
+
)
i(t)=I
m
⋅cos(ωt+ϕ
i
)
Where:
V
m
= Maximum voltage amplitude
I
m
= Maximum current amplitude
ω = Angular frequency (radians per second)
ϕ
v
= Phase angle of voltage
ϕ
i
= Phase angle of current
Then the instantaneous power can be calculated as:
=
⋅
⋅
cos
(
+
)
⋅
cos
(
+
)
P
inst
=V
m
⋅I
m
⋅cos(ωt+ϕ
v
)⋅cos(ωt+ϕ
i
)
Average Power in A.C. Circuits:
While instantaneous power provides information about power at a specific instant, average power is often more relevant and useful. In A.C. circuits, the average power over a complete cycle is generally of interest. For sinusoidal waveforms, the average power (
P
avg
) can be calculated as:
=
1
2
⋅
⋅
⋅
cos
(
−
)
P
avg
=
2
1
⋅V
m
⋅I
m
⋅cos(ϕ
v
−ϕ
i
)
Where
−
ϕ
v
−ϕ
i
is the phase angle difference between voltage and current.
Power Factor:
The power factor (
PF
PF) of an A.C. circuit is the ratio of the real power (average power) to the apparent power. Mathematically:
PF
=
Real Power
Apparent Power
PF=
Apparent Power
Real Power
Power factor is an important parameter in A.C. circuits, as it indicates the efficiency of power transfer and utilization in the circuit. It also helps in determining the phase relationship between voltage and current.
In summary, instantaneous power in A.C. circuits refers to the power at a specific moment in time, and it varies with the instantaneous values of voltage and current. Average power, on the other hand, provides a more practical measure of power over a complete cycle, and power factor helps assess the efficiency of power utilization in A.C. systems.