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10.6 Chapter summary (ESCQ2)

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

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

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

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

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

Real batteries have an internal resistance.

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*} 
The external resistance in the circuit is referred to as the load.
Physical Quantities  
Quantity  Unit name  Unit symbol 
Current (\(I\))  Amperes  \(\text{A}\) 
Electrical energy (\(E\))  Joules  \(\text{J}\) 
Power (\(P\))  Watts  \(\text{W}\) 
Resistance (\(R\))  Ohms  \(\text{Ω}\) 
Voltage / Potential difference (\(V\))  Volts  \(\text{V}\) 
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