Electrical capacity and capacitors

Содержание и основные понятия

The capacitor consists of two conductors separated by a dielectric, and its capacity shows which charge creates the specified voltage.
GEF · 10 grade
PIF · Baseline
Interactive model
capacitor
electrical capacity
Dieter
Field energy
01
The physical picture
What happens and what boundaries the model has.
Main message
The capacitor consists of two conductors separated by a dielectric, and its capacity shows which charge creates the specified voltage.
The capacity is determined by geometry and dielectricity, not by current charge.
When the container is connected in parallel, it is folded.
The power of the charged capacitor is contained in the electric field.
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.
C
=
q
U
C=\frac{q}{U}
C
=
U
q
​
electrical capacity
W
=
C
U
2
2
W=\frac{CU^2}{2}
W
=
2
C
U
2
​
Capacitor energy
Review of the situation
Double voltage on the constant capacitor quadruples the stored energy.
04
Links and application
In the real world
Double voltage on the constant capacitor quadruples the stored energy.
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 "Electricity and capacitors" through the model, not just the formula.
Outcome 2
Clear and correct use of terms: capacitor, electrical capacity, dielectric.
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.
capacitor
A system of two conductors separated by dielectrics designed to accumulate charge and energy from the field.
electrical capacity
The ratio of the charge of the conductor or condenser to its potential or voltage, as appropriate.
Dieter
A substance in which the charges are connected and the outer field is mainly polarized.
Field energy
Energy contained in the physical field and capable of being transferred to the substance or other fields.
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.
C
=
q
U
C=\frac{q}{U}
C
=
U
q
​
definition
Electrical capacity.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
q
∝
U
q\propto U
q
∝
U
For a linear condenser of this geometry, the charge of the plates is proportional to the voltage.
C
≡
q
U
C\equiv\frac{q}{U}
C
≡
U
q
​
The ratio of this proportionality is defined as the electrical capacity.
q
=
C
U
q=CU
q
=
C
U
The capacity characterizes geometry and dialectic rather than current values of q and U separately.
Conditions:
Linear capacitor with constant geometry and dielectricity; q is a single lining charge module, U 0 is the tension between the linings.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
W
=
C
U
2
2
W=\frac{CU^2}{2}
W
=
2
C
U
2
​
model effect
Condenser power.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
U
(
q
)
=
q
C
U(q)=\frac{q}{C}
U
(
q
)
=
C
q
​
During charging, the linear capacitor voltage increases with the accumulated charge.
W
=
∫
0
Q
U
(
q
)
d
q
=
∫
0
Q
q
C
d
q
=
Q
2
2
C
W=\int_0^Q U(q)\,dq=\int_0^Q\frac{q}{C}\,dq=\frac{Q^2}{2C}
W
=
∫
0
Q
​
U
(
q
)
d
q
=
∫
0
Q
​
C
q
​
d
q
=
2
C
Q
2
​
The operation of the source at the transport of small charges is stored as field energy.
Q
=
C
U
⇒
W
=
C
U
2
2
Q=CU\quad\Rightarrow\quad W=\frac{CU^2}{2}
Q
=
C
U
⇒
W
=
2
C
U
2
​
The charging and voltage connection is in the required shape.
Conditions:
Linear capacitor with constant C capacity, quasi-static charge; loss and radiation are not accounted for.
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
You can't change the formula to any situation just because it's a coincidence of letters. The key condition of this subject is that the capacity is determined by geometry and dielectricity, not the current charge.
How to Check the Mind
If the container is connected in parallel, then check the unit, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Electrical capacity and capacitors
The capacitor consists of two conductors separated by a dielectric, and its capacity shows which charge creates the specified voltage.
The capacity is determined by geometry and dielectricity, not by current charge.
When the container is connected in parallel, it is folded.
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.