## 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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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
1 change two variables in expr
1. 4087145886; locally 8922008:
$$V = I R$$
$$pdg_{6599} = pdg_{4501} pdg_{6458}$$
1. 2867848403:
$$I$$
$$pdg_{4501}$$
2. 1323602089:
$$I_1$$
$$pdg_{3978}$$
3. 7191277455:
$$R$$
$$pdg_{6458}$$
4. 5258419993:
$$R_1$$
$$pdg_{8697}$$
1. 4128500715; locally 8148802:
$$V = I_1 R_1$$
$$pdg_{6599} = pdg_{3978} pdg_{8697}$$
valid 4087145886:
4128500715:
4087145886:
4128500715:
10 declare final expr
1. 1457415749; locally 8713399:
$$\frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2}$$
$$\frac{1}{pdg_{1908}} = \frac{1}{pdg_{8697}} + \frac{1}{pdg_{3461}}$$
no validation is available for declarations 1457415749:
1457415749:
5 declare initial expr
1. 6753224061; locally 3843569:
$$I_{\rm total} = I_1 + I_2$$
$$pdg_{9647} = pdg_{3978} + pdg_{4856}$$
no validation is available for declarations 6753224061:
6753224061:
current flows through both resistors
7 divide both sides by
1. 2271186630; locally 8002723:
$$V = I_{\rm total} R_{\rm total}$$
$$pdg_{6599} = pdg_{1908} pdg_{9647}$$
1. 6546594355:
$$R_{\rm total}$$
$$pdg_{1908}$$
1. 2809345867; locally 1708642:
$$\frac{V}{R_{\rm total}} = I_{\rm total}$$
$$\frac{pdg_{6599}}{pdg_{1908}} = pdg_{9647}$$
valid 2271186630:
2809345867:
2271186630:
2809345867:
9 divide both sides by
1. 4866160902; locally 6759349:
$$\frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2}$$
$$\frac{pdg_{6599}}{pdg_{1908}} = \frac{pdg_{6599}}{pdg_{8697}} + \frac{pdg_{6599}}{pdg_{3461}}$$
1. 3433441359:
$$V$$
$$pdg_{6599}$$
1. 1457415749; locally 8713399:
$$\frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2}$$
$$\frac{1}{pdg_{1908}} = \frac{1}{pdg_{8697}} + \frac{1}{pdg_{3461}}$$
valid 4866160902:
1457415749:
4866160902:
1457415749:
8 substitute LHS of three expressions into expr
1. 2809345867; locally 1708642:
$$\frac{V}{R_{\rm total}} = I_{\rm total}$$
$$\frac{pdg_{6599}}{pdg_{1908}} = pdg_{9647}$$
2. 2051901211; locally 5168370:
$$\frac{V}{R_1} = I_1$$
$$\frac{pdg_{6599}}{pdg_{8697}} = pdg_{3978}$$
3. 7002609475; locally 4037937:
$$\frac{V}{R_2} = I_2$$
$$\frac{pdg_{6599}}{pdg_{3461}} = pdg_{4856}$$
4. 6753224061; locally 3843569:
$$I_{\rm total} = I_1 + I_2$$
$$pdg_{9647} = pdg_{3978} + pdg_{4856}$$
1. 4866160902; locally 6759349:
$$\frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2}$$
$$\frac{pdg_{6599}}{pdg_{1908}} = \frac{pdg_{6599}}{pdg_{8697}} + \frac{pdg_{6599}}{pdg_{3461}}$$
no check performed 2809345867:
2051901211:
7002609475: failed
6753224061:
4866160902:
2809345867:
2051901211:
7002609475: N/A
6753224061:
4866160902:
4 divide both sides by
1. 4128500715; locally 8148802:
$$V = I_1 R_1$$
$$pdg_{6599} = pdg_{3978} pdg_{8697}$$
1. 5181421075:
$$R_1$$
$$pdg_{8697}$$
1. 2051901211; locally 5168370:
$$\frac{V}{R_1} = I_1$$
$$\frac{pdg_{6599}}{pdg_{8697}} = pdg_{3978}$$
valid 4128500715:
2051901211:
4128500715:
2051901211:
6 change two variables in expr
1. 4087145886; locally 8922008:
$$V = I R$$
$$pdg_{6599} = pdg_{4501} pdg_{6458}$$
1. 9053099840:
$$I$$
$$pdg_{4501}$$
2. 7798615279:
$$I_{\rm total}$$
$$pdg_{9647}$$
3. 1100332145:
$$R$$
$$pdg_{6458}$$
4. 7410124465:
$$R_{\rm total}$$
$$pdg_{1908}$$
1. 2271186630; locally 8002723:
$$V = I_{\rm total} R_{\rm total}$$
$$pdg_{6599} = pdg_{1908} pdg_{9647}$$
valid 4087145886:
2271186630:
4087145886:
2271186630:
2 change two variables in expr
1. 4087145886; locally 8922008:
$$V = I R$$
$$pdg_{6599} = pdg_{4501} pdg_{6458}$$
1. 5585739998:
$$I$$
$$pdg_{4501}$$
2. 5463275819:
$$I_2$$
$$pdg_{4856}$$
3. 1377431959:
$$R$$
$$pdg_{6458}$$
4. 9746066299:
$$R_2$$
$$pdg_{3461}$$
1. 9243879541; locally 6313158:
$$V = I_2 R_2$$
$$pdg_{6599} = pdg_{3461} pdg_{4856}$$
valid 4087145886:
9243879541: failed
4087145886:
9243879541: N/A
3 divide both sides by
1. 9243879541; locally 6313158:
$$V = I_2 R_2$$
$$pdg_{6599} = pdg_{3461} pdg_{4856}$$
1. 3031116098:
$$R_2$$
$$pdg_{3461}$$
1. 7002609475; locally 4037937:
$$\frac{V}{R_2} = I_2$$
$$\frac{pdg_{6599}}{pdg_{3461}} = pdg_{4856}$$
valid 9243879541: failed
7002609475: failed
9243879541: N/A
7002609475: N/A
Physics Derivation Graph: Steps for total electrical resistance for circuit with two resistors in parallel

## Symbols for this derivation

symbol ID category latex scope dimension name value Used in derivations references
1908 variable R_{\rm total}
$$R_{\rm total}$$
real
• electric charge: -2
• length: 2
• mass: 1
• time: -1
electrical resistance
9
4501 variable I
$$I$$
real
• electric charge: 1
• time: -1
electric current
9
8697 variable R_1
$$R_1$$
real
• electric charge: -2
• length: 2
• mass: 1
• time: -1
electrical resistance
10
6458 variable R
$$R$$
real
• electric charge: -2
• length: 2
• mass: 1
• time: -1
electrical resistance
6
4856 variable I_2
$$I_2$$
real
• electric charge: 1
• time: -1
electric current
4
3978 variable I_1
$$I_1$$
real
• electric charge: 1
• time: -1
electric current
4
9647 variable I_{\rm total}
$$I_{\rm total}$$
real
• electric charge: 1
• time: -1
electric current
4
6599 variable V
$$V$$
real
• electric charge: -1
• length: 2
• mass: 1
• time: -2
voltage
11
3461 variable R_2
$$R_2$$
real
• electric charge: -2
• length: 2
• mass: 1
• time: -1
electrical resistance
10
MESSAGES:
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