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Andrew Carter

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Series Combination of Resistors

To produce more complex networks whose equivalent resistance is a combination of the individual resistors, individual resistors can be connected together in a series connection, a parallel connection or combinations of both series and parallel together.

Whenever the same current physically flows through both of the elements, two elements are said to be in series. Resistors are said to be connected in series when they are daisy chained together in a single line. Because all the current flowing through the first resistor has no other way to go, it must also pass through the second resistor and the third and so on, as seen in the image below.

Serially Connected Resistors

Serially Connected Resistors

In the series resistor circuit shown below, the resistors are connected in series and the same current passes through each resistor in the chain; and the total resistance (RT) of the circuit must be equal to the sum of all the individual resistors.

Resistors in Series

Resistors in Series

R_t = R_1 +R_2 + R_3

By taking the individual values of the resistors in the above sample, the total equivalent resistance required is equivalent to 9,000 Ohms. With a single equivalent resistor having a value of 9,000 Ohms, the three individual resistors can be replaced. RT will still be the sum of all the individual resistors connected together whether 4, 5 or even more resistors are all connected together. The equivalent resistance will be greater when more resistors are added to the series. Equivalent Resistance is the general term used for the total resistance and is defined as a single value of resistance that can replace any number of resistors in series without altering the values of the voltage or current in the circuit.

The amount of current that flows through a set of resistors in series is the same at all points in a series circuit, but the voltage across each resistor will be proportional to its resistance. The potential difference (voltage) seen across the network is the sum of those voltages, thus the total resistance can be found as the sum of those resistances. The voltage across each resistor connected in series follows different rules to that of series current.

The voltage, current or resistance of any series connected circuit can easily be found by using Ohm’s Law. Without affecting the total resistance, current or power to each resistor, resistors of a series circuit can be interchanged. The series resistor networks can also be thought of as voltage dividers and a series resistor circuit having N-resistive components will have N-different voltages across it while maintaining a common current. For any resistor Rx in the circuit, the voltage drop across that resistor is Vx = I*Rx.

I_R_1 = I_R_2 = I_R_3 = 1 mA

V_t = V_R_1 + V_R_2 + V_R_3 + … V_n

From the example below, the equivalent resistance, series current, voltage drop and power for each resistor can be calculated. The data can be presented in a tabular form in order to make life a little easier. Using Ohm’s Law, all the data can be obtained.

References
http://www.electronics-tutorials.ws/resistor/res_3.html

Tags: resistors in series

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