Question
Fri June 08, 2012 By: Vishnuraj

# how can we identify series and parallel connections easily.please specify the different ways for identifying that ?and also how to find the equivalent resistance of a circuit which is highly complex?

Fri June 08, 2012

### Resistors in Series

Resistors in series are equivalent to having one long resistor. If the properties of two resistors are equivalent, except the length, the final resistance will be the sum of the two construction methods:



This means that the resistors add when in series.


• Christmas tree lights are usually connected in series, with the unfortunate effect that if one light blows, the others will all go out (This happens because the circuit is not complete, if a circuit is not complete then the current cannot flow, hence the light bulbs all go out). However, most modern Christmas light strings have built in shunt resistors in parallel to the bulb, so that current will flow past the blown light bulb.

### Resistors in Parallel

In a parallel circuit, current is divided among multiple paths. This means that two resistors in parallel have a lower equivalent resistance than either of the parallel resistors, since both resistors allow current to pass. Two resistors in parallel will be equivalent to a resistor that is twice as wide:



Since conductances (the inverse of resistance) add in parallel, you get the following equation:



For example, two 4 ? resistors in parallel have an equivalent resistance of only 2 ?.

To simplify mathematical equations, resistances in parallel can be represented with two vertical lines "||" (as in geometry). For two resistors the parallel formula simplifies to:


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