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total electrical resistance for circuit with two resistors in series

Generated by the Physics Derivation Graph. Eq. \ref{eq:3843961} is an initial equation. \begin{equation} V = I R \label{eq:3843961} \end{equation} Change variable \(V\) to \(V_1\) and \(R\) to \(R_1\) in Eq. \ref{eq:3843961}; yields Eq. \ref{eq:8012785}. I is the same across both resistors \begin{equation} V_1 = I R_1 \label{eq:8012785} \end{equation} Change variable \(V\) to \(V_2\) and \(R\) to \(R_2\) in Eq. \ref{eq:3843961}; yields Eq. \ref{eq:6379878}. \begin{equation} V_2 = I R_2 \label{eq:6379878} \end{equation} Eq. \ref{eq:1124189} is an initial equation. voltage is measured across both resistors \begin{equation} V_{\rm total} = V_1 + V_2 \label{eq:1124189} \end{equation} Eq. \ref{eq:4107950} is an initial equation. \begin{equation} V_{\rm total} = I R_{\rm total} \label{eq:4107950} \end{equation} Substitute LHS of Eq. \ref{eq:4107950} and LHS of Eq. \ref{eq:8012785} and LHS of Eq. \ref{eq:6379878} into Eq. \ref{eq:1124189}; yields Eq. \ref{eq:4870091}. \begin{equation} I R_{\rm total} = I R_1 + I R_2 \label{eq:4870091} \end{equation} Divide both sides of Eq. \ref{eq:4870091} by \(I\); yields Eq. \ref{eq:5454988}. \begin{equation} R_{\rm total} = R_1 + R_2 \label{eq:5454988} \end{equation} Eq. \ref{eq:5454988} is one of the final equations.