Almost every time we need to combine resistors in series or in parallel connection so frequently that it needs some special attention.

*Make sure to read what is dc circuit first.*## Series Resistors Theory

Analyzing a series resistor circuit can be done with Kirchhoff's laws like before.

Consider a single-loop circuit in Figure.(1) as the example of series connection.

Consider a single-loop circuit in Figure.(1) as the example of series connection.

Figure 1. Series resistors |

*i*flows in both of them.

Applying Ohm's law to each resistor, we get

(6) |

*a-b*.

Figure 2. Series resistor equivalent circuit |

An equivalent circuit like Figure.(2) is very useful in simplifying the analysis of a circuit. In general,

Theequivalent resistanceof any number of resistors connected in series is the sum of the individual resistances.

For

*N*resistors in series then,(7) |

In order to determine the voltage in each resistor in Figure.(2) then we substitute Equation.(3) into (1) and get

(8) |

## Voltage Divider

The source voltage

*v*is divided among the resistors in direct proportion to their resistances; the larger the resistance, the larger the voltage drop. This is called the*principle of voltage division*and the circuit in Figure.(1) is called a*voltage divider*. In general, if voltage divider has N resistors (*R*_{1},*R*) in series with the voltage source_{2}, ....,R_{N}*v*, the*n*th resistor will have a voltage drop of(9) |

The voltage divider is used to divide a large voltage to a smaller one.

Have you understood what is series resistor? Don't forget to share and subscribe! Happy learning!

*Reference: Fundamentals of electric circuits by Charles K. Alexander and Matthew N. O. Sadiku*

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