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

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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
1 declare initial expr
  1. 4087145886; locally 3843961:
    \(V = I R\)
    \(pdg_{6599} = pdg_{4501} pdg_{6458}\)
no validation is available for declarations 4087145886:
4087145886:
2 change two variables in expr
  1. 4087145886; locally 3843961:
    \(V = I R\)
    \(pdg_{6599} = pdg_{4501} pdg_{6458}\)
  1. 2698469612:
    \(V\)
    \(pdg_{6599}\)
  2. 9830343096:
    \(V_1\)
    \(pdg_{8257}\)
  3. 7774819339:
    \(R\)
    \(pdg_{6458}\)
  4. 9174439158:
    \(R_1\)
    \(pdg_{8697}\)
  1. 7675171493; locally 8012785:
    \(V_1 = I R_1\)
    \(pdg_{8257} = pdg_{4501} pdg_{8697}\)
valid 4087145886:
7675171493:
4087145886:
7675171493:
I is the same across both resistors
3 change two variables in expr
  1. 4087145886; locally 3843961:
    \(V = I R\)
    \(pdg_{6599} = pdg_{4501} pdg_{6458}\)
  1. 7497687256:
    \(V\)
    \(pdg_{6599}\)
  2. 1608399874:
    \(V_2\)
    \(pdg_{8721}\)
  3. 5890617067:
    \(R\)
    \(pdg_{6458}\)
  4. 1484794622:
    \(R_2\)
    \(pdg_{3461}\)
  1. 6061695358; locally 6379878:
    \(V_2 = I R_2\)
    \(pdg_{8721} = pdg_{3461} pdg_{4501}\)
valid 4087145886:
6061695358:
4087145886:
6061695358:
4 declare initial expr
  1. 9063568209; locally 1124189:
    \(V_{\rm total} = V_1 + V_2\)
    \(pdg_{4691} = pdg_{8257} + pdg_{8721}\)
no validation is available for declarations 9063568209:
9063568209:
voltage is measured across both resistors
5 declare initial expr
  1. 4939880586; locally 4107950:
    \(V_{\rm total} = I R_{\rm total}\)
    \(pdg_{4691} = pdg_{1908} pdg_{4501}\)
no validation is available for declarations 4939880586:
4939880586:
6 substitute LHS of three expressions into expr
  1. 4939880586; locally 4107950:
    \(V_{\rm total} = I R_{\rm total}\)
    \(pdg_{4691} = pdg_{1908} pdg_{4501}\)
  2. 7675171493; locally 8012785:
    \(V_1 = I R_1\)
    \(pdg_{8257} = pdg_{4501} pdg_{8697}\)
  3. 6061695358; locally 6379878:
    \(V_2 = I R_2\)
    \(pdg_{8721} = pdg_{3461} pdg_{4501}\)
  4. 9063568209; locally 1124189:
    \(V_{\rm total} = V_1 + V_2\)
    \(pdg_{4691} = pdg_{8257} + pdg_{8721}\)
  1. 2715678478; locally 4870091:
    \(I R_{\rm total} = I R_1 + I R_2\)
    \(pdg_{1908} pdg_{4501} = pdg_{3461} pdg_{4501} + pdg_{4501} pdg_{8697}\)
no check performed 4939880586:
7675171493:
6061695358:
9063568209:
2715678478:
4939880586:
7675171493:
6061695358:
9063568209:
2715678478:
7 divide both sides by
  1. 2715678478; locally 4870091:
    \(I R_{\rm total} = I R_1 + I R_2\)
    \(pdg_{1908} pdg_{4501} = pdg_{3461} pdg_{4501} + pdg_{4501} pdg_{8697}\)
  1. 7844317489:
    \(I\)
    \(pdg_{4501}\)
  1. 7217021879; locally 5454988:
    \(R_{\rm total} = R_1 + R_2\)
    \(pdg_{1908} = pdg_{3461} + pdg_{8697}\)
valid 2715678478:
7217021879: dimensions are consistent
2715678478:
7217021879: N/A
8 declare final expr
  1. 7217021879; locally 5454988:
    \(R_{\rm total} = R_1 + R_2\)
    \(pdg_{1908} = pdg_{3461} + pdg_{8697}\)
no validation is available for declarations 7217021879: dimensions are consistent
7217021879: N/A
Physics Derivation Graph: Steps for total electrical resistance for circuit with two resistors in series

Symbols for this derivation

See also all 212 symbols
symbol ID category latex scope dimension name value Used in derivations references
8721 variable V_2
\(V_2\)
real
  • length: 2
  • time: -2
  • mass: 1
  • charge: -1
voltage 3
8257 variable V_1
\(V_1\)
real
  • length: 2
  • time: -2
  • mass: 1
  • charge: -1
voltage 3
1908 variable R_{\rm total}
\(R_{\rm total}\)
real
  • length: 2
  • time: -1
  • mass: 1
  • charge: -2
electrical resistance 9
3461 variable R_2
\(R_2\)
real
  • length: 2
  • time: -1
  • mass: 1
  • charge: -2
electrical resistance 10
4501 variable I
\(I\)
real
  • time: -1
  • charge: 1
electric current 9
6599 variable V
\(V\)
real
  • length: 2
  • time: -2
  • mass: 1
  • charge: -1
voltage 11
6458 variable R
\(R\)
real
  • length: 2
  • time: -1
  • mass: 1
  • charge: -2
electrical resistance 6
4691 variable V_{\rm total}
\(V_{\rm total}\)
real
  • length: 2
  • time: -2
  • mass: 1
  • charge: -1
voltage 2
8697 variable R_1
\(R_1\)
real
  • length: 2
  • time: -1
  • mass: 1
  • charge: -2
electrical resistance 10
MESSAGE: