Switch current

Содержание и основные понятия

The synusoidal current changes direction from time to time. The current is equal to the constant current that produces the same average power in the resistor.
GEF · 11 grade
PIF · Baseline
Interactive model
variable current
Current value
Phase shift
Sensitivity
01
The physical picture
What happens and what boundaries the model has.
Main message
The synusoidal current changes direction from time to time. The current is equal to the constant current that produces the same average power in the resistor.
The resistor does not change the current phase relative to the voltage.
The coil is holding the current, the capacitor is ahead of phase.
The resonance of tension arises from the equality of inductive and capacitive resistance.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
I
д
=
I
m
2
I_{\text{д}}=\frac{I_m}{\sqrt2}
I
d
​
=
2
​
I
m
​
​
current
X
L
=
ω
L
,
X
C
=
1
ω
C
X_L=\omega L,\qquad X_C=\frac{1}{\omega C}
X
L
​
=
ω
L
,
X
C
​
=
ω
C
1
​
Missile resistance
Review of the situation
The voltage of the household network 230 V is active; the sinusoid amplitude is approximately 2 times greater.
04
Links and application
In the real world
The voltage of the household network 230 V is active; the sinusoid amplitude is approximately 2 times greater.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Transformed current" through the model, not just the formula.
Outcome 2
Select and correctly use terms: AC, current, phase shift.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
variable current
Electrical current, the size and usually the direction of which changes periodically over time.
Current value
The constant current or voltage value giving the same thermal effect as the AC considered.
Phase shift
Different phases of two harmonic variations of the same frequency.
Sensitivity
A sharp increase in forced fluctuations in the proximity of the frequency to the system ' s own frequency.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
I
д
=
I
m
2
I_{\text{д}}=\frac{I_m}{\sqrt2}
I
d
​
=
2
​
I
m
​
​
model effect
Current current.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
I
д
:
=
1
T
∫
0
T
i
2
(
t
)
d
t
I_{\text{д}}:=\sqrt{\frac{1}{T}\int_0^T i^2(t)\,dt}
I
d
​
:=
T
1
​
∫
0
T
​
i
2
(
t
)
d
t
​
The current value is defined as the medium quadratic giving the same resistor heat as DC.
i
(
t
)
=
I
m
cos
⁡
ω
t
i(t)=I_m\cos\omega t
i
(
t
)
=
I
m
​
cos
ω
t
For sinusoidal current, the square is I_m2cos2\t.
⟨
cos
⁡
2
ω
t
⟩
=
1
2
⇒
I
д
=
I
m
2
\langle\cos^2\omega t\rangle=\frac12\quad\Rightarrow\quad I_{\text{д}}=\frac{I_m}{\sqrt2}
⟨
cos
2
ω
t
⟩
=
2
1
​
⇒
I
d
​
=
2
​
I
m
​
​
The average cosine over the whole period is one second.
Conditions:
A strict sinusoidal fixed current; averaging is carried out for a whole number of periods.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
X
L
=
ω
L
,
X
C
=
1
ω
C
X_L=\omega L,\qquad X_C=\frac{1}{\omega C}
X
L
​
=
ω
L
,
X
C
​
=
ω
C
1
​
model effect
Reactivated resistance.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
u
L
=
L
d
i
d
t
u_L=L\frac{di}{dt}
u
L
​
=
L
d
t
d
i
​
For sinusoidal current, the derivative amplitude is equal to \I_m, so U_{Lm}=\LI_m.
X
L
:
=
U
L
m
I
m
=
ω
L
X_L:=\frac{U_{Lm}}{I_m}=\omega L
X
L
​
:=
I
m
​
U
L
m
​
​
=
ω
L
The ratio of voltage and current amplitude determines the inductive resistance.
i
=
C
d
u
C
d
t
⇒
X
C
:
=
U
C
m
I
m
=
1
ω
C
i=C\frac{du_C}{dt}\quad\Rightarrow\quad X_C:=\frac{U_{Cm}}{I_m}=\frac{1}{\omega C}
i
=
C
d
t
d
u
C
​
​
⇒
X
C
​
:=
I
m
​
U
C
m
​
​
=
ω
C
1
​
Similarly, the capacitor current gives a capacitance resistance, inversely proportional frequency.
Conditions:
The installed sinusoidal mode with an angle frequency of x; ideal linear L and C without active loss.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
The key condition of this subject is that the Resistor does not change the current phase relative to the voltage.
How to Check the Mind
The coil holds the current, the capacitor is ahead of phase. Then check the unit, vector direction, and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Switch current
The synusoidal current changes direction from time to time. The current is equal to the constant current that produces the same average power in the resistor.
The resistor does not change the current phase relative to the voltage.
The coil is holding the current, the capacitor is ahead of phase.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.