In the late 1800s, DC could not be easily converted to high voltages. This is useful for many large appliances like dishwashers, refrigerators, and so on, which run on AC. Motors and generators are the exact same device, but motors convert electrical energy into mechanical energy (if the shaft on a motor is spun, a voltage is generated at the terminals!). AC can be converted to and from high voltages easily using transformers.ĪC is also capable of powering electric motors. Higher voltages mean lower currents, and lower currents mean less heat generated in the power line due to resistance. At high voltages (over 110kV), less energy is lost in electrical power transmission. This is because generating and transporting AC across long distances is relatively easy. Home and office outlets are almost always AC. Even though, in our example, we had the voltage varying from -170V to 170V, the root mean square is 120V RMS. It is often helpful to use the RMS value for AC when you want to calculate electrical power. To accomplish that, we use a method called "Root mean squared." (RMS). How? When talking about AC (since the voltage changes constantly), it is often easier to use an average or mean. NOTE: You might have heard that AC voltage in the US is 120V. If we were to measure the voltage in our outlets with an oscilloscope, this is what we would see ( WARNING: do not attempt to measure the voltage in an outlet with an oscilloscope! This will likely damage the equipment). Additionally, 60 cycles of the sine wave occurs every second. Notice that, as we predicted, the voltage rise up to 170V and down to -170V periodically. We can plug these numbers into our formula to get the equation (remember that we are assuming our phase is 0): In the United States, the power provided to our homes is AC with about 170V zero-to-peak (amplitude) and 60Hz (frequency). We can turn to our trusty outlet for a good example of how an AC waveform works. For simplicity, we sill assume that phase is 0° for the rest of this tutorial. Because of the periodic nature of the sine wave, if the wave form is shifted by 360° it becomes the same waveform again, as if it was shifted by 0°.
It is often given as a number between 0 and 360 and measured in degrees. Phase is a measure of how shifted the waveform is with respect to time. T is our independent variable: time (measured in seconds). The frequency tells how many times a particular wave form (in this case, one cycle of our sine wave - a rise and a fall) occurs within one second. This is given in the form of hertz or units per second. The sin() function indicates that our voltage will be in the form of a periodic sine wave, which is a smooth oscillation around 0V.Ģπ is a constant that converts the freqency from cycles (in hertz) to angular frequnecy (radians per second).į describes the frequency of the sine wave. This describes the maximum voltage that our sine wave can reach in either direction, meaning that our voltage can be +V P volts, -V P volts, or somewhere in between. The equation to the right of the equals sign describes how the voltage changes over time. V(t) is our voltage as a function of time, which means that our voltage changes as time changes.
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