Physics Derivation Graph: review derivation: total electrical resistance for circuit with two resistors in parallel

review derivation: total electrical resistance for circuit with two resistors in parallel

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Notes for this derivation:
http://www.dfcd.net/articles/derivations/resistors.html

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Physics Derivation Graph: Steps for total electrical resistance for circuit with two resistors in parallel
Index	Inference Rule	Input latex	Feeds latex	Output latex	step validity	dimension check	unit check	notes
1	change two variables in expr	4087145886; locally 8922008: $V = I R$ $p d g_{6599} = p d g_{4501} p d g_{6458}$	2867848403: $I$ $p d g_{4501}$ 1323602089: $I_{1}$ $p d g_{3978}$ 7191277455: $R$ $p d g_{6458}$ 5258419993: $R_{1}$ $p d g_{8697}$	4128500715; locally 8148802: $V = I_{1} R_{1}$ $p d g_{6599} = p d g_{3978} p d g_{8697}$	valid	4087145886: 4128500715:	4087145886: 4128500715:
10	declare final expr	1457415749; locally 8713399: $\frac{1}{R_{t o t a l}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$ $\frac{1}{p d g_{1908}} = \frac{1}{p d g_{8697}} + \frac{1}{p d g_{3461}}$			no validation is available for declarations	1457415749:	1457415749:
5	declare initial expr			6753224061; locally 3843569: $I_{t o t a l} = I_{1} + I_{2}$ $p d g_{9647} = p d g_{3978} + p d g_{4856}$	no validation is available for declarations	6753224061:	6753224061:	current flows through both resistors
7	divide both sides by	2271186630; locally 8002723: $V = I_{t o t a l} R_{t o t a l}$ $p d g_{6599} = p d g_{1908} p d g_{9647}$	6546594355: $R_{t o t a l}$ $p d g_{1908}$	2809345867; locally 1708642: $\frac{V}{R_{t o t a l}} = I_{t o t a l}$ $\frac{p d g_{6599}}{p d g_{1908}} = p d g_{9647}$	valid	2271186630: 2809345867:	2271186630: 2809345867:
9	divide both sides by	4866160902; locally 6759349: $\frac{V}{R_{t o t a l}} = \frac{V}{R_{1}} + \frac{V}{R_{2}}$ $\frac{p d g_{6599}}{p d g_{1908}} = \frac{p d g_{6599}}{p d g_{8697}} + \frac{p d g_{6599}}{p d g_{3461}}$	3433441359: $V$ $p d g_{6599}$	1457415749; locally 8713399: $\frac{1}{R_{t o t a l}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$ $\frac{1}{p d g_{1908}} = \frac{1}{p d g_{8697}} + \frac{1}{p d g_{3461}}$	valid	4866160902: 1457415749:	4866160902: 1457415749:
8	substitute LHS of three expressions into expr	2809345867; locally 1708642: $\frac{V}{R_{t o t a l}} = I_{t o t a l}$ $\frac{p d g_{6599}}{p d g_{1908}} = p d g_{9647}$ 2051901211; locally 5168370: $\frac{V}{R_{1}} = I_{1}$ $\frac{p d g_{6599}}{p d g_{8697}} = p d g_{3978}$ 7002609475; locally 4037937: $\frac{V}{R_{2}} = I_{2}$ $\frac{p d g_{6599}}{p d g_{3461}} = p d g_{4856}$ 6753224061; locally 3843569: $I_{t o t a l} = I_{1} + I_{2}$ $p d g_{9647} = p d g_{3978} + p d g_{4856}$		4866160902; locally 6759349: $\frac{V}{R_{t o t a l}} = \frac{V}{R_{1}} + \frac{V}{R_{2}}$ $\frac{p d g_{6599}}{p d g_{1908}} = \frac{p d g_{6599}}{p d g_{8697}} + \frac{p d g_{6599}}{p d g_{3461}}$	no check performed	2809345867: 2051901211: 7002609475: failed 6753224061: 4866160902:	2809345867: 2051901211: 7002609475: N/A 6753224061: 4866160902:
4	divide both sides by	4128500715; locally 8148802: $V = I_{1} R_{1}$ $p d g_{6599} = p d g_{3978} p d g_{8697}$	5181421075: $R_{1}$ $p d g_{8697}$	2051901211; locally 5168370: $\frac{V}{R_{1}} = I_{1}$ $\frac{p d g_{6599}}{p d g_{8697}} = p d g_{3978}$	valid	4128500715: 2051901211:	4128500715: 2051901211:
6	change two variables in expr	4087145886; locally 8922008: $V = I R$ $p d g_{6599} = p d g_{4501} p d g_{6458}$	9053099840: $I$ $p d g_{4501}$ 7798615279: $I_{t o t a l}$ $p d g_{9647}$ 1100332145: $R$ $p d g_{6458}$ 7410124465: $R_{t o t a l}$ $p d g_{1908}$	2271186630; locally 8002723: $V = I_{t o t a l} R_{t o t a l}$ $p d g_{6599} = p d g_{1908} p d g_{9647}$	valid	4087145886: 2271186630:	4087145886: 2271186630:
2	change two variables in expr	4087145886; locally 8922008: $V = I R$ $p d g_{6599} = p d g_{4501} p d g_{6458}$	5585739998: $I$ $p d g_{4501}$ 5463275819: $I_{2}$ $p d g_{4856}$ 1377431959: $R$ $p d g_{6458}$ 9746066299: $R_{2}$ $p d g_{3461}$	9243879541; locally 6313158: $V = I_{2} R_{2}$ $p d g_{6599} = p d g_{3461} p d g_{4856}$	valid	4087145886: 9243879541: failed	4087145886: 9243879541: N/A
3	divide both sides by	9243879541; locally 6313158: $V = I_{2} R_{2}$ $p d g_{6599} = p d g_{3461} p d g_{4856}$	3031116098: $R_{2}$ $p d g_{3461}$	7002609475; locally 4037937: $\frac{V}{R_{2}} = I_{2}$ $\frac{p d g_{6599}}{p d g_{3461}} = p d g_{4856}$	valid	9243879541: failed 7002609475: failed	9243879541: N/A 7002609475: N/A

Symbols for this derivation

See also all 227 symbols

symbol ID	category	latex	scope	dimension	name	Used in derivations	references
3461	variable	R_2 $R_{2}$	real	electric charge: -2 length: 2 mass: 1 time: -1	electrical resistance	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	Electrical_resistance_and_conductance	10
4501	variable	I $I$	real	electric charge: 1 time: -1	electric current	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	Electric_current	9
3978	variable	I_1 $I_{1}$	real	electric charge: 1 time: -1	electric current	total electrical resistance for circuit with two resistors in parallel	Electric_current	4
9647	variable	I_{\rm total} $I_{t o t a l}$	real	electric charge: 1 time: -1	electric current	total electrical resistance for circuit with two resistors in parallel	Electric_current	4
8697	variable	R_1 $R_{1}$	real	electric charge: -2 length: 2 mass: 1 time: -1	electrical resistance	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	Electrical_resistance_and_conductance	10
4856	variable	I_2 $I_{2}$	real	electric charge: 1 time: -1	electric current	total electrical resistance for circuit with two resistors in parallel	Electric_current	4
6599	variable	V $V$	real	electric charge: -1 length: 2 mass: 1 time: -2	voltage	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	Voltage	11
6458	variable	R $R$	real	electric charge: -2 length: 2 mass: 1 time: -1	electrical resistance	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	Electrical_resistance_and_conductance	6
1908	variable	R_{\rm total} $R_{t o t a l}$	real	electric charge: -2 length: 2 mass: 1 time: -1	electrical resistance	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	Electrical_resistance_and_conductance	9

MESSAGES:

local variable 'all_df' referenced before assignment
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