Wiring connections

Содержание и основные понятия

The connection method determines the current and voltage distribution. Equivalent resistance replaces a complex fragment with one calculation element.
GEF · Grade 8
PIF · Baseline
Interactive model
sequence connection
parallel connection
Equivalent resistance
Scheme
01
The physical picture
What happens and what boundaries the model has.
Main message
The connection method determines the current and voltage distribution. Equivalent resistance replaces a complex fragment with one calculation element.
The currents are the same when connected in sequence and the voltages add up.
At a parallel connection, the voltage is the same and the total current is the sum of the currents of the branches.
The household appliances are connected in parallel to operate independently at the same network voltage.
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.
R
=
R
1
+
R
2
R=R_1+R_2
R
=
R
1
​
+
R
2
​
sequence connection
1
R
=
1
R
1
+
1
R
2
\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}
R
1
​
=
R
1
​
1
​
+
R
2
​
1
​
parallel connection
Review of the situation
Two identical 10 ohm resistors give 20 ohms in sequence and 5 ohm in parallel.
04
Links and application
In the real world
Two identical 10 ohm resistors give 20 ohms in sequence and 5 ohm in parallel.
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 "Construction of Guides" through the model, not just through the formula.
Outcome 2
Distinguish and correctly use the terms: sequence connection, parallel connection equivalent resistance.
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.
sequence connection
Combination of elements without spreading through which the same current passes through them.
parallel connection
Combination of components between the common two knots at which the voltage is the same.
Equivalent resistance
Resistance of one replacement component that retains a connection between the general current and the voltage of the chain section.
Scheme
Conditional graphic representation of electrical circuit components and their connections.
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.
R
=
R
1
+
R
2
R=R_1+R_2
R
=
R
1
​
+
R
2
​
model effect
A consistent connection.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
I
=
I
1
=
I
2
I=I_1=I_2
I
=
I
1
​
=
I
2
​
The same current passes through the connected elements.
U
=
U
1
+
U
2
=
I
R
1
+
I
R
2
U=U_1+U_2=IR_1+IR_2
U
=
U
1
​
+
U
2
​
=
I
R
1
​
+
I
R
2
​
The total voltage is equal to the sum of the cell voltage drops.
I
R
=
I
(
R
1
+
R
2
)
⇒
R
=
R
1
+
R
2
IR=I(R_1+R_2)\Rightarrow R=R_1+R_2
I
R
=
I
(
R
1
​
+
R
2
​
)
⇒
R
=
R
1
​
+
R
2
​
Equivalent resistance shall give the same total voltage at the same current.
Conditions:
The two omic elements are connected consecutively without branches; resistance to wires and contacts is ignored.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
1
R
=
1
R
1
+
1
R
2
\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}
R
1
​
=
R
1
​
1
​
+
R
2
​
1
​
model effect
A parallel connection.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
U
=
U
1
=
U
2
U=U_1=U_2
U
=
U
1
​
=
U
2
​
Both parallel branches are connected to one pair of knots and have the same voltage.
I
=
I
1
+
I
2
=
U
R
1
+
U
R
2
I=I_1+I_2=\frac{U}{R_1}+\frac{U}{R_2}
I
=
I
1
​
+
I
2
​
=
R
1
​
U
​
+
R
2
​
U
​
The current in the node is divided between branches, and the current of each branch is determined by the law of Oma.
U
R
=
U
(
1
R
1
+
1
R
2
)
\frac{U}{R}=U\left(\frac{1}{R_1}+\frac{1}{R_2}\right)
R
U
​
=
U
(
R
1
​
1
​
+
R
2
​
1
​
)
The equivalent element consumes the same common current at the same voltage as the conductive formula.
Conditions:
The two omic elements are connected simultaneously to the same two nodes; the steady state mode, the connecting wires are ideal.
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 transfer the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that the currents are the same when the current is connected in sequence and the voltages add up.
How to Check the Mind
At a parallel connection, the voltage is the same and the total current is equal to the sum of the currents of the branches. Then check the units, the direction of the vectors and the behaviour of the result at zero or very large parameter.
Detached chains and Kirhgoff rules
For the node, the charge is maintained: the sum of the input currents is equal to the amount of output. For a closed loop, the amount is zero. These rules are the common method of calculating the branched circuits; the sequence and parallel connections are their private cases. In the 8th class, the quality of application is sufficient, the full calculation is for deepening.
Σ
Conclusion on the topic
Wiring connections
The connection method determines the current and voltage distribution. Equivalent resistance replaces a complex fragment with one calculation element.
The currents are the same when connected in sequence and the voltages add up.
At a parallel connection, the voltage is the same and the total current is the sum of the currents of the branches.
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.