13 - Conduction - Multiple Resistances

\[\begin{aligned} Q &= Q_1+ Q_2 + Q_3 = \frac{T_A-T_B}{R_1} + \frac{T_A-T_B}{R_2} + \frac{T_A-T_B}{R_3} \\ &= (T_A-T_B)\left(\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \right) \\ &= \frac{T_A-T_B}{R} \end{aligned}\] where \[\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\]