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Voltage Dividers A series circuit acts as a voltage divider. You will learn what this term means and why voltage dividers are an important application of series circuits. After completing this section, you should be able to: Use a series circuit as a voltage divider Apply the voltage-divider formula Use the potentiometer as an adjustable voltage divider Describe some voltage-divider applications To illustrate how a series string of resistors acts as a voltage divider, we will examine Figure 16, where there are two resistors in series. As you already know, there are two voltage drops: one across R1 and one across R2. We call these voltage drops V1 and V2, respectively, as indicated in the diagram. FIGURE 16 Two-resistor voltage divider. + I R1 V1 - Vs + R2 V2 - Since the same current flows through each resistor, the voltage drops are proportional to the resistance values. For example, if the value of R2 is twice that of R1, then the value of V2 is twice that of V1. In other words, the total voltage drop divides among the series resistors in amounts directly proportional to the resistance values. For example, in Figure 16, if VS is 10 V, R1 is 50 , and R2 is 100 , then V1 is onethird the total voltage, or 3.33 V, because R1 is one-third the total resistance. Likewise, V2 is two-thirds VS, or 6.67 V. Voltage-Divider Formula With a few calculations, a formula for determining how the voltages divide among series resistors can be developed. I = V1 also I = V2 and I = VS where RT = R1 + R2 R1 R2 RT V2 = VS from which V2 = VS x R2 and V1 = VS x R1 This only applies if R2 is not R2 RT R1+R2 R1+R2 loaded. 11 Current-Divider Formula for Two Branches The reason for doing so is that two parallel resistors are often found in practical circuits. We start by restating the formula for the total resistance of two parallel branches. RT = R1R2 also V = I1R1, V = I2R2 and V = ITRT R1 + R2 Figure 17 IT I1 Vs R1 I2 I1R1= ITRT I1 = R1R2 x IT (R1+ R2)x R1 I1 = R2 x IT (R1+ R2) R2 Also I2R2= ITRT I2 = R1R2 x IT (R1+ R2)x R2 I2 = R1 x IT (R1+ R2) 12