Here are some examples of complicated circuits which cannot be reduced to a series circuit or a parallel circuit. One cannot find equivalent resistances using the rules from resistors in series or in parallel. Instead, Kirchhoff's Current and Voltage Laws are used to solve these circuits.

Figure 1 This is an example of a Wheatstone Bridge
circuit, where the component labelled 'G' is a galvanometer. This type
of circuit is used to calculate the resistance of an unknown resistor,
RX. The other three resistors are variable. |

Figure 2 This circuit can be thought of as a 'T-circuit'.
It cannot be reduced to series or parallel combinations of resistors because
there is more than one emf source. |

Kirchhoff's Laws are not the only method of solving such circuits. Different methods have arisen to solve complicated circuits, such as the Superposition Theorem. Some of these methods are easier to use than others, and their simplicity is dependent on the specific circuit to be solved.

The Wheatstone Bridge is
a fundamental circuit originally invented to measure resistance. To see
how this works look at the following simulated Wheatstone Bridge Experiment.
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