The bridge and the potentiometer in code

You will write four functions for the metre bridge and the potentiometer. They follow the lesson.

The idea. On a metre bridge, $\dfrac{R}{S} = \dfrac{l}{100 - l}$. The percentage error in $R$ from an error $\Delta l$ in the balance point is $\dfrac{100\,\Delta l}{l(100 - l)} \times 100$. On a potentiometer, the emfs are in the ratio of the balance lengths, and the internal resistance is $r = R\,\dfrac{l_1 - l_2}{l_2}$.

Your tasks.

1. In bridge_resistance, return the unknown resistance in the left gap for a known resistance S in the right gap and the balance length l in cm.
2. In bridge_error, return the percentage error in $R$ for a balance point l and an error dl, both in cm.
3. In emf_ratio, return $E_1/E_2$ for the balance lengths of two cells.
4. In internal_resistance, return $r$ for the resistance R and the two balance lengths l1 and l2.