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total electrical resistance for circuit with two resistors in parallel

Generated by the Physics Derivation Graph. Change variable \(I\) to \(I_1\) and \(R\) to \(R_1\) in Eq. \ref{eq:8922008}; yields Eq. \ref{eq:8148802}. \begin{equation} V = I_1 R_1 \label{eq:8148802} \end{equation} Change variable \(I\) to \(I_2\) and \(R\) to \(R_2\) in Eq. \ref{eq:8922008}; yields Eq. \ref{eq:6313158}. \begin{equation} V = I_2 R_2 \label{eq:6313158} \end{equation} Divide both sides of Eq. \ref{eq:6313158} by \(R_2\); yields Eq. \ref{eq:4037937}. \begin{equation} \frac{V}{R_2} = I_2 \label{eq:4037937} \end{equation} Divide both sides of Eq. \ref{eq:8148802} by \(R_1\); yields Eq. \ref{eq:5168370}. \begin{equation} \frac{V}{R_1} = I_1 \label{eq:5168370} \end{equation} Eq. \ref{eq:3843569} is an initial equation. current flows through both resistors \begin{equation} I_{\rm total} = I_1 + I_2 \label{eq:3843569} \end{equation} Change variable \(I\) to \(I_{\rm total}\) and \(R\) to \(R_{\rm total}\) in Eq. \ref{eq:8922008}; yields Eq. \ref{eq:8002723}. \begin{equation} V = I_{\rm total} R_{\rm total} \label{eq:8002723} \end{equation} Divide both sides of Eq. \ref{eq:8002723} by \(R_{\rm total}\); yields Eq. \ref{eq:1708642}. \begin{equation} \frac{V}{R_{\rm total}} = I_{\rm total} \label{eq:1708642} \end{equation} Substitute LHS of Eq. \ref{eq:1708642} and LHS of Eq. \ref{eq:5168370} and LHS of Eq. \ref{eq:4037937} into Eq. \ref{eq:3843569}; yields Eq. \ref{eq:6759349}. \begin{equation} \frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2} \label{eq:6759349} \end{equation} Divide both sides of Eq. \ref{eq:6759349} by \(V\); yields Eq. \ref{eq:8713399}. \begin{equation} \frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2} \label{eq:8713399} \end{equation} Eq. \ref{eq:8713399} is one of the final equations.