Series and parallel connections — lesson. Science State Board, Class 10.

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Series connection of parallel resistors:

A series-parallel circuit is formed by connecting a set of parallel resistors in series.

Connect \(R_1\) and \(R_2\) in parallel to obtain an effective resistance of \(R_{P1}\).
Similarly, connect \(R_3\) and \(R_4\) in parallel to get an effective resistance of \(R_{P2}\).
These parallel segments of resistors are then joined in series.

Series-parallel combination of resistors

The formula for the effective resistance of the parallel combination of resistors is

\frac{1}{R_{P}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

For two resistors in the circuit, the effective resistance is given as

\begin{array}{l} \frac{1}{R_{P1}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \\ \frac{1}{R_{P2}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \end{array}

Using the effective resistance of the series circuit,

R_{S} = R_{1} + R_{2} + R_{3}

, the net effective resistance of the series-parallel combination of resistors is,

R_{Total} = R_{P1} + R_{P2}

Parallel connection of series resistors:

A parallel-series circuit is formed by connecting a set of series resistors in parallel.

Connect \(R_1\) and \(R_2\) in series to get an effective resistance of \(R_{S1}\).
Similarly, connect \(R_3\) and \(R_4\) in series to get an effective resistance of \(R_{S2}\).
These series segments of resistors are then joined in parallel.