Review Derivation: Physics Derivation Graph

Return to navigation page or list derivations

Review total electrical resistance for circuit with two resistors in series

abstract:
reference: http://www.dfcd.net/articles/derivations/resistors.html

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4087145886 $V = I R$	no validation is available for declarations
Note about step 2: I is the same across both resistors
2	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 $V = I R$	9174439158 $R_1$ 7774819339 $R$ 9830343096 $V_1$ 2698469612 $V$	7675171493 $V_1 = I R_1$	LHS diff is pdg0006599 - pdg0008257 RHS diff is pdg0004501*(pdg0006458 - pdg0008697)
3	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 $V = I R$	1484794622 $R_2$ 5890617067 $R$ 1608399874 $V_2$ 7497687256 $V$	6061695358 $V_2 = I R_2$	LHS diff is pdg0006599 - pdg0008721 RHS diff is pdg0004501*(-pdg0003461 + pdg0006458)
Note about step 4: voltage is measured across both resistors
4	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			9063568209 $V_{\rm total} = V_1 + V_2$	no validation is available for declarations
5	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4939880586 $V_{\rm total} = I R_{\rm total}$	no validation is available for declarations
6	0000111246: substitute LHS of three expressions into expression number of inputs: 4; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} into Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}.	9063568209 $V_{\rm total} = V_1 + V_2$ 6061695358 $V_2 = I R_2$ 7675171493 $V_1 = I R_1$ 4939880586 $V_{\rm total} = I R_{\rm total}$		2715678478 $I R_{\rm total} = I R_1 + I R_2$	recognized infrule but not yet supported
7	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	2715678478 $I R_{\rm total} = I R_1 + I R_2$	7844317489 $I$	7217021879 $R_{\rm total} = R_1 + R_2$	valid
8	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	7217021879 $R_{\rm total} = R_1 + R_2$			no validation is available for declarations

Symbols used in total electrical resistance for circuit with two resistors in series

0000004501: $ I $
0000006458: $ R $
0000008697: $ R_1 $
0000003461: $ R_2 $
0000001908: $ R_{\rm total} $
0000006599: $ V $
0000008257: $ V_1 $
0000008721: $ V_2 $
0000004691: $ V_{\rm total} $

d3js visualization of steps and expressions in total electrical resistance for circuit with two resistors in series

Hold the mouse over a node to highlight that node and its neighbors. You can zoom in/out. You can pan the image. You can move nodes by clicking and dragging.

Actions: Edit Derivation

You must be logged in to edit the steps of derivation, edit the abstract, or rename the derivation.

Generate Tex file or PDF file

Delete Derivation and all associated steps

You must be logged in to delete the derivation.

timing of Neo4j queries:

0.003 seconds for pdg_app/to_review_derivation 70b59d9c-4b95-48d6-8cf9-dce1fa1ba871
0.003 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivation19709984-a337-4a37-af24-758bdc713af8
0.003 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_ID19709984-a337-4a37-af24-758bdc713af8
0.003 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUT19709984-a337-4a37-af24-758bdc713af8
0.003 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEED19709984-a337-4a37-af24-758bdc713af8
0.004 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUT19709984-a337-4a37-af24-758bdc713af8
0.002 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_step19709984-a337-4a37-af24-758bdc713af8
0.004 seconds for pdg_app/ 70b59d9c-4b95-48d6-8cf9-dce1fa1ba871

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4087145886 \(V = I R\)	no validation is available for declarations
Note about step 2: I is the same across both resistors
2	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 \(V = I R\)	9174439158 \(R_1\) 7774819339 \(R\) 9830343096 \(V_1\) 2698469612 \(V\)	7675171493 \(V_1 = I R_1\)	LHS diff is pdg0006599 - pdg0008257 RHS diff is pdg0004501*(pdg0006458 - pdg0008697)
3	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 \(V = I R\)	1484794622 \(R_2\) 5890617067 \(R\) 1608399874 \(V_2\) 7497687256 \(V\)	6061695358 \(V_2 = I R_2\)	LHS diff is pdg0006599 - pdg0008721 RHS diff is pdg0004501*(-pdg0003461 + pdg0006458)
Note about step 4: voltage is measured across both resistors
4	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			9063568209 \(V_{\rm total} = V_1 + V_2\)	no validation is available for declarations
5	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4939880586 \(V_{\rm total} = I R_{\rm total}\)	no validation is available for declarations
6	0000111246: substitute LHS of three expressions into expression number of inputs: 4; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} into Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}.	9063568209 \(V_{\rm total} = V_1 + V_2\) 6061695358 \(V_2 = I R_2\) 7675171493 \(V_1 = I R_1\) 4939880586 \(V_{\rm total} = I R_{\rm total}\)		2715678478 \(I R_{\rm total} = I R_1 + I R_2\)	recognized infrule but not yet supported
7	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	2715678478 \(I R_{\rm total} = I R_1 + I R_2\)	7844317489 \(I\)	7217021879 \(R_{\rm total} = R_1 + R_2\)	valid
8	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	7217021879 \(R_{\rm total} = R_1 + R_2\)			no validation is available for declarations