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Review total electrical resistance for circuit with two resistors in parallel

step inference rule input feed output step validity (as per SymPy)
1
  • 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}.
  1. 4087145886
    \(V = I R\)
  1. 5258419993
    \(R_1\)
  2. 7191277455
    \(R\)
  3. 1323602089
    \(I_1\)
  4. 2867848403
    \(I\)
  1. 4128500715
    \(V = I_1 R_1\)
 LHS diff is 0 RHS diff is -pdg0003978*pdg0008697 + pdg0004501*pdg0006458
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}.
  1. 4087145886
    \(V = I R\)
  1. 9746066299
    \(R_2\)
  2. 1377431959
    \(R\)
  3. 5463275819
    \(I_2\)
  4. 5585739998
    \(I\)
  1. 9243879541
    \(V = I_2 R_2\)
 LHS diff is 0 RHS diff is -pdg0003461*pdg0004856 + pdg0004501*pdg0006458
3
  • 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}.
  1. 9243879541
    \(V = I_2 R_2\)
  1. 3031116098
    \(R_2\)
  1. 7002609475
    \(\frac{V}{R_2} = I_2\)
 valid
4
  • 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}.
  1. 4128500715
    \(V = I_1 R_1\)
  1. 5181421075
    \(R_1\)
  1. 2051901211
    \(\frac{V}{R_1} = I_1\)
 valid
Note about step 5: current flows through both resistors
5
  • 0000111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an initial equation.
  1. 6753224061
    \(I_{\rm total} = I_1 + I_2\)
 no validation is available for declarations
6
  • 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}.
  1. 4087145886
    \(V = I R\)
  1. 7410124465
    \(R_{\rm total}\)
  2. 1100332145
    \(R\)
  3. 7798615279
    \(I_{\rm total}\)
  4. 9053099840
    \(I\)
  1. 2271186630
    \(V = I_{\rm total} R_{\rm total}\)
 LHS diff is 0 RHS diff is -pdg0001908*pdg0009647 + pdg0004501*pdg0006458
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}.
  1. 2271186630
    \(V = I_{\rm total} R_{\rm total}\)
  1. 6546594355
    \(R_{\rm total}\)
  1. 2809345867
    \(\frac{V}{R_{\rm total}} = I_{\rm total}\)
 valid
8
  • 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}.
  1. 6753224061
    \(I_{\rm total} = I_1 + I_2\)
  2. 7002609475
    \(\frac{V}{R_2} = I_2\)
  3. 2051901211
    \(\frac{V}{R_1} = I_1\)
  4. 2809345867
    \(\frac{V}{R_{\rm total}} = I_{\rm total}\)
  1. 4866160902
    \(\frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2}\)
 recognized infrule but not yet supported
9
  • 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}.
  1. 4866160902
    \(\frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2}\)
  1. 3433441359
    \(V\)
  1. 1457415749
    \(\frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2}\)
 valid
10
  • 0000111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\ref{eq:#1} is one of the final equations.
  1. 1457415749
    \(\frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2}\)
no validation is available for declarations

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