This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
http://www.dfcd.net/articles/derivations/resistors.html
Index | Inference Rule | Input latex | Feeds latex | Output latex | step validity | dimension check | unit check | notes |
---|---|---|---|---|---|---|---|---|
1 | change two variables in expr |
|
|
|
valid |
4087145886:
4128500715: |
4087145886:
4128500715: |
|
10 | declare final expr |
|
|
|
no validation is available for declarations |
1457415749:
|
1457415749:
|
|
5 | declare initial expr |
|
|
|
no validation is available for declarations |
6753224061:
|
6753224061:
|
current flows through both resistors |
7 | divide both sides by |
|
|
|
valid |
2271186630:
2809345867: |
2271186630:
2809345867: |
|
9 | divide both sides by |
|
|
|
valid |
4866160902:
1457415749: |
4866160902:
1457415749: |
|
8 | substitute LHS of three expressions into expr |
|
|
|
no check performed |
2809345867:
2051901211: 7002609475: failed 6753224061: 4866160902: |
2809345867:
2051901211: 7002609475: N/A 6753224061: 4866160902: |
|
4 | divide both sides by |
|
|
|
valid |
4128500715:
2051901211: |
4128500715:
2051901211: |
|
6 | change two variables in expr |
|
|
|
valid |
4087145886:
2271186630: |
4087145886:
2271186630: |
|
2 | change two variables in expr |
|
|
|
valid |
4087145886:
9243879541: failed |
4087145886:
9243879541: N/A |
|
3 | divide both sides by |
|
|
|
valid |
9243879541:
failed 7002609475: failed |
9243879541:
N/A 7002609475: N/A |
symbol ID | category | latex | scope | dimension | name | value | Used in derivations | references | |
---|---|---|---|---|---|---|---|---|---|
3978 | variable |
I_1
\(I_1\) |
real |
|
electric current | 4 | |||
1908 | variable |
R_{\rm total}
\(R_{\rm total}\) |
real |
|
electrical resistance | 9 | |||
8697 | variable |
R_1
\(R_1\) |
real |
|
electrical resistance | 10 | |||
3461 | variable |
R_2
\(R_2\) |
real |
|
electrical resistance | 10 | |||
9647 | variable |
I_{\rm total}
\(I_{\rm total}\) |
real |
|
electric current | 4 | |||
6599 | variable |
V
\(V\) |
real |
|
voltage | 11 | |||
4501 | variable |
I
\(I\) |
real |
|
electric current | 9 | |||
6458 | variable |
R
\(R\) |
real |
|
electrical resistance | 6 | |||
4856 | variable |
I_2
\(I_2\) |
real |
|
electric current | 4 |