Admittance, which is usually represented by Y, describes how easily an electrical current can flow through a device or in a circuit. It is also the reciprocal of inductance. In a direct current circuit, where current is being pumped through the circuit at a constant rate, inductance is equivalent to resistance, which is a measure of how difficult it is for an electrical current to flow through a device. Just as resistance has a unit of measurement—the ohm—admittance also has a unit of measurement—the siemen. Using Ohm's Law and the rules of the metric system, it is possible to use an admittance value in microsiemens along with a current value to find a voltage value in millivolts.

## From Siemens to Resistance

Consider a simple, closed DC circuit that has a battery with unknown voltage, a current of I = 2 amps and a resistor, labeled R, showing an admittance of Y = 2 siemens. To solve for the voltage, we must first invert the admittance to find the resistance of the resistor. Therefore, R = 1/Y = 1/2 = 0.5 ohms.

## From Resistance to Voltage

Now that we know the resistance and the current in the circuit, we can use Ohm's Law to solve for the voltage across the resistor. Ohm's Law states that the voltage across the resistor is equal to the resistance multiplied by the current, or V = R_I. Therefore, as R = 0.5 ohms and I = 2 amps, then V = 0.5_2 = 1 volt. Because this is a simple, closed circuit, the voltage across the resistor equals the voltage across the battery.

## The Metric System

Every country throughout the world, except for Liberia, Myanmar and the United States, uses a measurement system known as the metric system. One main reason this system is so popular is that it is a decimal system: every measurement is scaled by a factor of ten, and each scale has a prefix to represent it. Additionally, each type of measurement has a base unit, such as the meter for length or the gram for mass. By attaching a prefix to a base unit, you can describe the magnitude of a measurement. For example, the prefix 'milli' comes from the Latin word for 'thousandth'. Therefore, a millimeter would be the same length as 1/1,000 of a meter. Additionally, 'micro' is Latin for 'small', which is fitting because a micrometer is 1/1,000,000 of a meter.

## Putting It All Together

Given a simple, closed DC circuit, it is possible to use current and admittance values to find the voltage across a device in the circuit directly. For example, if this device is a resistor with an admittance of Y = 1 microsiemen, and the current flowing through the circuit is I = 1 amp, then we can combine Ohm's Law, V = R*I, with the fact that R = 1/Y to show that V = I/Y, or that voltage is equal to the current divided by the admittance. By plugging in the current and admittance values, we can calculate V = (1 amp)/(1 microsiemen) = 1,000,000 volts. From here we can convert the answer into millivolts by using the fact that milli means 1/1,000. Therefore, 1,000,000 volts is the same as 1,000,000,000 millivolts.

#### References

- U.S. Metric Association: SI Prefixes and Their Etymologies
- U.S. Metric Association: Commonly Used Metric System Units, Symbols, and Prefixes
- Geekologie: Countries That Don't Use The Metric System
- U.S. Metric Association: Metric Usage and Metrication in Other Countries
- The Electrical Engineering Handbook; Richard C. Dorf; 1997
- Basic Concepts of Electrical Engineering; Kuldeep Sahay, Shivendra Pathak; 2006

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