To solve such circuits, first reduce the parallel branches to an equivalent series branch and then solve the circuit as a simple series circuit. In the circuit shown below, we can see that resistors R 2 and R 3 are connected in parallel with each other and that both are connected in series with R 1. In this circuit some of the elements are connected in series fashion and some are in parallel. If we add and we get which confirms Kirchoff’s current law.A series-parallel circuitis a combination of series and parallel circuits. Therefore, the potential difference acrossĮxample 3: Complex circuits (containing series and parallel sections)Ĭ) What is the potential difference across each resistor?ĭ) What is the current through each resistor?Ī) First the equivalent effective resistance of the parallel section is determined and then added to the other series components:Ĭ) Using and the resistance for each series component or parallel section: This means that the same voltage (V) is dropped across all components in a parallel circuit. In these cases, the parallel sections are best dealt with first, followed by the series sections.Ī) Calculate the effective equivalent resistance of the circuit:ī) Calculate the current flowing through the circuit:Ĭ) Calculate the potential difference across :ī) Using and the total resistance for the circuit:ī) Calculate the total current flowing through the circuit:Ĭ) What is the potential difference across :ī) Using and the total resistance for the circuit:Ĭ) As it is a simple parallel circuit, the potential difference across and will be the same and equal to the potential difference supplied to the circuit: All of the resistors, as well as the battery, are connected between these two sets of points. The equivalent effective resistance of a parallel circuit is given by:Ĭomplex problems may involve circuits that have both series and parallel sections.
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