Summary and Main Ideas

Summary

1. Ohm's Law governs the relationship between current and potential difference for a circuit element at constant temperature. Mathematically we write \(I=\frac{V}{R}\).

2. Conductors that obey Ohm's Law are called ohmic conductors; those that do not are called non-ohmic conductors.

3. Ohm's Law can be applied to a single circuit element or the circuit as a whole (if the components are ohmic).

4. The equivalent resistance of resistors in series (\({R}_{s}\)) can be calculated as follows: \({R}_{s}={R}_{\text{1}}+{R}_{\text{2}}+{R}_{\text{3}}+...+{R}_{n}\)

5. The equivalent resistance of resistors in parallel (\({R}_{p}\)) can be calculated as follows: \(\frac{\text{1}}{{R}_{p}}=\frac{\text{1}}{{R}_{\text{1}}}+\frac{\text{1}}{{R}_{\text{2}}}+\frac{\text{1}}{{R}_{\text{3}}}+...+\frac{\text{1}}{{R}_{n}}\)

6. Real batteries have an internal resistance.

7. The potential difference \(V\) of the battery is related to its emf \(\mathcal{E}\) and internal resistance \(r\) by:

   \begin{align*} \mathcal{E}& = V_{\text{load}} + V_{\text{internal resistance}}\\ &\text{or} \\ \mathcal{E}& = IR_{Ext} + Ir \end{align*}

8. The external resistance in the circuit is referred to as the load.