Lecture 34 Instantaneous and average power 1 Why care about power Currents and voltages are the fundamental variables in linear circuits However in many practical cases we do not care about low level variables All we care about is the power being generated and where it is going Brightness of a lightbulb Heat in an electric stove Strength of transmitted received signals Electric grid distributes power to network nodes houses cities Etc Power can be found from voltage and current but not the other way around It is often easier to study the power flows in a circuit rather than the voltages and currents 2 Instantaneous power In general the power being consumed at a given point in time is Pinst t v t i t where the voltage and current must follow the passive sign convention The above is always true but it can change very fast 3 Average power So what we really care about is the amount of power being consumed in AVERAGE Just like any other function power can be averaged by integrating its instantaneous value over a very long interval and dividing by the length of the interval However if the function is periodic it is not necessary to integrate over a very long interval One period denoted T in the formula below is sufficient 4 Average power in SSS In sinusoidal steady state there is a simpler way to find the average power being consumed 5 Interesting cases Resistor i t v t R so We say that current and voltage are in phase Capacitor i t C v t so We say that current leads voltage by 90 degrees Inductor v t L i t so We say that current lags voltage by 90 degrees 6 Example 7 8
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