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total electrical resistance for circuit with two resistors in series

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