5.2d Combining resistors

Solving circuits

To solve a circuit is a lot like solving an equation. You have a situation with some knowns and some unknowns, and you must use your knowledge of physics to know the unknowns and find out everything about a circuit. The concept of solving circuits is also known as circuit analysis or (in advanced forms) network analysis.

For a circuit to be solved you should know:

• The resistance of any part of a circuit (any component or combination of components)

• The current at any point in a circuit

• The potential difference between any two points in a circuit

The tools you have include:

• V = IR

• P = VI (and P = I²R and P = V²/R)

• The rules for combining components

• Kirchhoff's laws of circuit analysis (current law and voltage law) <--- see section 5.2e.

Combining resistors

The three minimum divisions of a working circuit are the supply, the cables and the load (control elements, such as switches, and meters, such as a voltmeter, are additional elements). In an ideal circuit the cables have no resistance. The supply may have a resistance (internal resistance, which we will look at in more detail later) and the load must have a resistance - unless energy transformation is occurring you do not have a useful circuit.

There are many components that can form part of the load, but in many cases we do not need to know the details when solving a circuit. Frequently, we can consider all components of the load in terms of their resistance only - and think of them as resistors.

A common first step in solving circuits is to determine the total resistance of a circuit. In order to do this, you must be able to determine the combined resistance of more than one resistor (or other component with a resistance). This may take several steps before you have the final value.

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