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Resistors
Resistors are electronic simple electronic components that limit the amount of electrical current that passes through them. Usually containing carbon or thin metal film, resistors provide a consistent, reliable amount of electrical resistance across a wide range of voltages and temperatures. Engineers measure resistance in units of ohms, and when you connect two or more resistors in a series circuit, one after another as in a daisy chain, the total resistance through all of them is the sum of the ohm values of each resistor. For example, a 10- and a 20-ohm resistor in series produce 30 ohms.
Kirchoff̵7;s Law
To reduce a voltage using resistors, it helps to know Kirchoff̵7;s law for voltage: The sum of all the voltage sources and voltage drops around a circuit loop always equals zero. For example, if you have a 1.5-V ̶0;D̶1; cell battery connected to a resistor, the loop consists of the battery and the resistor. The battery contributes 1.5 V to the circuit, so the resistor must have a voltage drop of 1.5 V; this is true regardless of the resistor̵7;s ohm value. If you use two resistors instead of one, the total drop across both is still 1.5 V; the drop across each is proportional to its resistance. Two 100-ohm resistors, for example, divide the voltage drop equally, so each one will have .75 V across it, for a total of 1.5 V. The same two 100-ohm resistors, with a 12-V source, have 6 V across each. By adjusting the value of the resistors, you obtain a drop of 9 V across one.
Calculation
To change 12 V to 9, you must determine what fraction 9 is of 12. By subtracting 9 from 12, you get 3, and you have two voltages that add up to 12 -- 3 and 9. The two numbers, 3 and 9, have a proportion of 1:3. For two resistors in series, one will have a resistance three times greater than the other. If you pick an easy resistance value, such as 1,000 ohms, the other resistor is three times that, or 3,000 ohms. You can place the two resistors in series, then connect a 12-V source across the resistor pair. The voltage across the 3,000-ohm resistor is 9 V.
Limits
When you place resistors across a voltage source, they use current. You can determine how much current by using Ohm̵7;s law -- written as "I = V/R" -- where "V" stands for volts, "I" represents current in amps and "R" is resistance in ohms. With 12 volts and 4,000 ohms total, the resistors have 12 divided by 4,000, or 3 milliamps, of current. Though 3 milliamps is gentle on a battery, eventually it will drain the battery. If you want the 9 V to power a motor, it takes much more current than the circuit provides. You can increase the current by reducing resistance, but at the expense of consuming more power in the resistors. If the resistance is too low, the resistors become hot and burn themselves up.