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
Clicking on the step index will take you to the page where you can edit that step.
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: 

2  change two variables in expr 



valid 
4087145886:
9243879541: 
4087145886:
9243879541: 

3  divide both sides by 



valid 
9243879541:
7002609475: 
9243879541:
7002609475: 

4  divide both sides by 



valid 
4128500715:
2051901211: 
4128500715:
2051901211: 

5  declare initial expr 



no validation is available for declarations 
6753224061:

6753224061:

current flows through both resistors 
6  change two variables in expr 



valid 
4087145886:
2271186630: 
4087145886:
2271186630: 

7  divide both sides by 



valid 
2271186630:
2809345867: 
2271186630:
2809345867: 

8  substitute LHS of three expressions into expr 



no check performed 
2809345867:
2051901211: 7002609475: 6753224061: 4866160902: 
2809345867:
2051901211: 7002609475: 6753224061: 4866160902: 

9  divide both sides by 



valid 
4866160902:
1457415749: dimensions are consistent 
4866160902:
1457415749: N/A 

10  declare final expr 



no validation is available for declarations 
1457415749:
dimensions are consistent 
1457415749:
N/A 
symbol ID  category  latex  scope  dimension  name  value  Used in derivations  references  

8697  variable 
R_1
\(R_1\) 
real 

electrical resistance  10  
6599  variable 
V
\(V\) 
real 

voltage  11  
9647  variable 
I_{\rm total}
\(I_{\rm total}\) 
real 

electric current  4  
3978  variable 
I_1
\(I_1\) 
real 

electric current  4  
4501  variable 
I
\(I\) 
real 

electric current  9  
3461  variable 
R_2
\(R_2\) 
real 

electrical resistance  10  
4856  variable 
I_2
\(I_2\) 
real 

electric current  4  
1908  variable 
R_{\rm total}
\(R_{\rm total}\) 
real 

electrical resistance  9  
6458  variable 
R
\(R\) 
real 

electrical resistance  6 