A cell balances at l₁ = 520.0 cm on a potentiometer…

Step 1. The line. $\dfrac{l_1}{l_2} = \dfrac{R + r}{R} = 1 + \dfrac{r}{R}$. A graph of $\dfrac{l_1}{l_2}$ against $\dfrac{1}{R}$ is a line with the slope $r$. The program in the Python solution fits it and finds a slope of $0.90\ \Omega$ and an intercept of $1.00$. Each pair also gives $r = R\,\dfrac{l_1 - l_2}{l_2} = 0.90\ \Omega$.

Step 2. The second cell. $E_2 = E_1\,\dfrac{390.0}{520.0}$ $= 1.50\ \text{V} \times 0.750$ $= 1.125\ \text{V}$, which is $1.13$ V.

Step 3. The terminal voltage. $V = E\,\dfrac{R}{R + r}$ $= 1.50\ \text{V} \times \dfrac{8\ \Omega}{8\ \Omega + 0.90\ \Omega}$ $= 1.35$ V.