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# Series Resistors and Voltage Divider

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. Figure 1. Series resistors
The two resistors are in series since the same current i flows in both of them.
Applying Ohm's law to each resistor, we get (1)
Apply KVL to the loop in the clockwise direction, we obtain (5)
Assuming those two resistors can be expressed by an equivalent resistor Req; so, (6)
Hence in Figure.(1) can be replaced by the equivalent circuit in Figure.(2). Those two are equivalent because they have the same values of voltages and current at the terminal 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,
The equivalent resistance of 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 (R1R2, ....,RN ) in series with the voltage source v, the nth resistor will have a voltage drop of (9)

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

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

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