Physics 10.14 - 10.16 - Series and parallel circuit design

How circuit layout changes net resistance

A circuit diagram is a model of electrical connections. It shows which components share the same route and where the route divides; it does not show the physical size or position of the laboratory apparatus.

Two quantities help us interpret the model:

• current, $I$, is the rate of flow of charge, measured in amperes ($\mathrm{A}$);
• potential difference, $V$, is the energy transferred per unit charge between two points, measured in volts ($\mathrm{V}$).

Resistance, $R$, describes how strongly a component opposes current. It is measured in ohms ($\Omega$). Charge and current are not used up by a resistor.

Resistors in series

Components are in series when they lie one after another in a single complete route. The same current passes through every series component. Each resistor opposes that same flow, so adding a second resistor adds another opposition in the route:

$R_{\text{total}} = R_{1} + R_{2}$

The net resistance is therefore greater than either individual resistance. At a fixed supply potential difference, the increased net resistance produces a smaller current.

Resistors in parallel

Components are in parallel when they lie on separate branches between the same two junctions. Each branch has the same potential difference across it. Adding a parallel branch gives charge an additional route, so the total current supplied increases at the same supply potential difference.

From $R = \frac{V}{I}$, a larger total current for the same potential difference means a smaller net resistance. With two resistors in parallel, the net resistance is less than the resistance of either branch. The resistance has not been "used up"; the circuit offers more conducting routes.

Calculating in series circuits

Three relationships are needed for a series circuit:

1. $I_{\text{total}} = I_{1} = I_{2}$: current is the same everywhere in the single route.
2. $V_{\text{supply}} = V_{1} + V_{2}$: the potential differences across the components add to the supply potential difference.
3. $R_{\text{total}} = R_{1} + R_{2}$: the series resistances add.