Lecture 341• Instantaneous and average powerWhy care about power?• Currents and voltages are the fundamental variables inlinear circuits.• However, in many practical cases we do not care aboutlow level variables. All we care about is the powerbeing 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 notthe other way around.• It is often easier to study the power flows in a circuit,rather than the voltages and currents2Instantaneous power• In general, the power being consumed at a given pointin time isPinst(t) = v(t)*i(t)where the voltage and current must follow the passivesign convention• The above is always true, but it can change very fast3Average power• So, what we really care about is the amount ofpower being consumed in AVERAGE• Just like any other function, power can beaveraged by integrating its instantaneous valueover a very long interval and dividing by thelength of the interval• However, if the function is periodic, it is notnecessary to integrate over a very long interval.One period (denoted T in the formula below) issufficient4Average power in SSS• In sinusoidal steady state, there is a simpler wayto find the average power being consumed5Interesting cases• Resistor: i(t) = v(t)/R, soWe say that current and voltage are “in phase”• Capacitor i(t) = C*v’(t), soWe say that current “leads” voltage by 90 degrees• Inductor v(t) = L*i’(t), soWe say that current “lags” voltage by 90
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