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Voltage divider circuitsVoltage dividerLet's analyze a simple series circuit, determining the voltage drops across individual resistors:
From the given values of individual resistances, we can determine a total circuit resistance, knowing that resistances add in series: From here, we can use Ohm's Law (I=E/R) to determine the total current, which we know will be the same as each resistor current, currents being equal in all parts of a series circuit: Now, knowing that the circuit current is 2 mA, we can use Ohm's Law (E=IR) to calculate voltage across each resistor: It should be apparent that the voltage drop across each resistor is proportional to its resistance, given that the current is the same through all resistors. Notice how the voltage across R_{2} is double that of the voltage across R_{1}, just as the resistance of R_{2} is double that of R_{1}. If we were to change the total voltage, we would find this proportionality of voltage drops remains constant: The voltage across R_{2} is still exactly twice that of R_{1}'s drop, despite the fact that the source voltage has changed. The proportionality of voltage drops (ratio of one to another) is strictly a function of resistance values. With a little more observation, it becomes apparent that the voltage drop across each resistor is also a fixed proportion of the supply voltage. The voltage across R_{1}, for example, was 10 volts when the battery supply was 45 volts. When the battery voltage was increased to 180 volts (4 times as much), the voltage drop across R_{1} also increased by a factor of 4 (from 10 to 40 volts). The ratio between R_{1}'s voltage drop and total voltage, however, did not change: Likewise, none of the other voltage drop ratios changed with the increased supply voltage either: Voltage divider formulaFor this reason a series circuit is often called a voltage divider for its ability to proportion  or divide  the total voltage into fractional portions of constant ratio. With a little bit of algebra, we can derive a formula for determining series resistor voltage drop given nothing more than total voltage, individual resistance, and total resistance: The ratio of individual resistance to total resistance is the same as the ratio of individual voltage drop to total supply voltage in a voltage divider circuit. This is known as the voltage divider formula, and it is a shortcut method for determining voltage drop in a series circuit without going through the current calculation(s) of Ohm's Law. Using this formula, we can reanalyze the example circuit's voltage drops in fewer steps:
Voltage dividers find wide application in electric meter circuits, where specific combinations of series resistors are used to "divide" a voltage into precise proportions as part of a voltage measurement device.


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