AC and EM waves - alternating currents &...

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Unformatted text preview: alternating currents & electromagnetic waves PHY232 Remco Zegers zegers@nscl.msu.edu Room W109 cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html PHY232 - Remco Zegers - alternating currents and electromagnetic waves 2 quiz (extra credit) At t=0, the switch is closed. Shortly after that: a) the current slowly increases from I=0 to I=V/R b) the current slowly decreases from I=V/R to I=0 c) the current is a constant I=V/R L I R V The coil opposes the flow of current due to self-inductance, so the current cannot immediately become the maximum I=V/R. It will slowly rise to this value PHY232 - Remco Zegers - alternating currents and electromagnetic waves 3 Alternating current circuits previously, we look at DC circuits (the voltage delivered by the source was constant). Now, we look at AC circuits, in which case the source is sinusoidal. A is used in circuits to denote the difference I R V I V R PHY232 - Remco Zegers - alternating currents and electromagnetic waves 4 A circuit with a resistor The voltage over the resistor is the same as the voltage delivered by the source: V R (t)=V sin t=V sin(2 ft) The current through the resistor is: I R (t)= V /R sin t Since V(t) and I(t) have the same behavior as a function of time, they are said to be in phase. V is the maximum voltage V(t) is the instantaneous voltage is the angular frequency; =2 f f: frequency (Hz) SET YOUR CALCULATOR TO RADIANS WHERE NECESSARY I V(t)=V sin t R I R (A) V =10 V R=2 Ohm =1 rad/s PHY232 - Remco Zegers - alternating currents and electromagnetic waves 5 lon-capa you should now do problem 1 from set 7. PHY232 - Remco Zegers - alternating currents and electromagnetic waves 6 rms currents/voltages To understand energy consumption by the circuit, it doesnt matter what the sign of the current/voltage is. We need the absolute average currents and voltages (root-mean-square values) : V rms =V max / 2 I rms =I max / 2 The following hold: V rms =I rms R V max =I max R I R (A) |I R| (A) |V R |(V) V rms I rms PHY232 - Remco Zegers - alternating currents and electromagnetic waves 7 power consumption by an AC circuit We already saw (DC): P=VI=V 2 /R=I 2 R For AC circuits with a single resistor: P(t)=V(t)*I(t)=V I sin 2 t The average power consumption: P ave =V rms *I rms =V 2 rms /R=I 2 rms R P ave =(V max / 2)( I max / 2)= I max V max /2 |I R| (A) |V R |(V) V rms I rms P(W) PHY232 - Remco Zegers - alternating currents and electromagnetic waves 8 vector representation time (s) V-V V The voltage or current as a function of time can be described by the projection of a vector rotating with constant angular velocity on one of the axes (x or y)....
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AC and EM waves - alternating currents &...

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