Voltage drop series circuits are used in direct and alternating current (DC and AC) devices to allow lower voltages than those supplied to the circuit to be used for specific purposes within the device. For example, a device with a 24volt DC battery may have an 18volt motor, 3.4volt lights and a 5volt control logic chip which all need steady supply voltages. The principle that allows calculating the parameters of these circuits is Kirchhoff's Voltage Law which states that the summation of all voltages within a series circuit must equal zero.
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Define the application. In the example above, a power implement with an 18volt motor, 3.4volt LED (light emitting diode) indicator lights and a 5volt controller chip has a 24volt rechargeable battery. Current to each of the devices is regulated by transistors that are referenced to a precision voltage drop circuit consisting of three resistors in series with the battery. With a knowledge of the voltage needs, you can calculate this voltage drop reference circuit.

Calculate an overall voltage drop resistance and current flow through the series circuit. As this is a reference voltage circuit, only very small currents are required to regulate the transistors, so set the total circuit resistance at 10,000 ohms (10kohm). Solve for current by dividing supply voltage (Vs) by total resistance (Rt). Substituting, 24 volts/10,000 ohms = 2.4 milliamps (0.0024 amps).

Calculate the proportion of total circuit resistance needed for the 3.4volt reference for the LED lights, since this is the lowest voltage, requiring the lowest resistance. The equation will be R lights = Rt(10kohms) X 3.4volt lights/24volt supply = 1416 ohms (1.416 kohms).

Calculate the proportion of the total circuit resistance needed for the 5volt logic chip. The equation will be R chip = Rt(10kohms) X 5volt chip/24volt supply = 2,083 ohms (2.083 kohms). Subtracting the first 1.416kohms resistor for the lights, all that is needed is a 2.083 minus 1.416 = 0.667k ohm or a 667ohm resistor to provide the 2.083kohm series resistance.

Calculate the proportion of the total circuit resistance that will be needed to provide the 18volt reference voltage for the motor. This will be the highest resistance required and is solved by the equation R motor = Rt(10kohms) X 18volt motor/24volt supply = 10 kohm X 0.75 = 7.5 kohms. Subtracting the 2.083 kohm resistance you already have, this will be a 7.5 k minus 2.083 k = 5.417 kohm resistor.

Calculate the summation of all three resistors which constitute a proportion of the total voltage drop of 24 volts over 10 kohms for the circuit. The equation: 1.416 kohms for the lights + 0.667 kohms for the chip + 5.417 kohms for the motor = 7.5 kohms total.

Determine the value of the final resistor that will bring total resistance up to 10 kohms by subtracting 7.5 k ohms from 10 kohms = 2.5 kohms (2,500 ohms).

Determine the intermediate voltages between each of the resistors in series (1.416 k + 0.667 k + 5.417 k + 2.5 k = 10 k compared to the negative of the 24volt supply (24volts). This results in voltage readings of +3.4volts, +5volts, +18volts and +24volts respectively, and the circuit resolves to zero per Kirchhoff's Voltage Law.
Tips & Warnings
 Using high impedance resistor voltage drop circuits conserves power.
 Installing resistors with too low an overall circuit ohm value can result in too much current flowing, and smoking and burning of electronic components.
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References
 Photo Credit digital multimeter 3 image by dinostock from Fotolia.com resistors image by Albert Lozano from Fotolia.com circuit board image by dwags from Fotolia.com