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AC and EM waves

# AC and EM waves - alternating currents electromagnetic...

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alternating currents & electromagnetic waves PHY232 Remco Zegers [email protected] Room W109 – cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html

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PHY232 - Remco Zegers - alternating currents and electromagnetic waves 2 quiz (extra credit) ¾ At t=0, the switch is closed. Shortly after that: ¾ a) the current slowly increases from I=0 to I=V/R ¾ b) the current slowly decreases from I=V/R to I=0 ¾ 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 ¾ previously, we look at DC circuits (the voltage delivered by the source was constant). ¾ 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

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PHY232 - Remco Zegers - alternating currents and electromagnetic waves 4 A circuit with a resistor ¾ The voltage over the resistor is the same as the voltage delivered by the source: V R (t)=V 0 sin ω t=V 0 sin(2 π ft) ¾ The current through the resistor is: I R (t)= V 0 /R sin ω t ¾ Since V(t) and I(t) have the same behavior as a function of time, they are said to be ‘in phase’. ¾ V 0 is the maximum voltage ¾ V(t) is the instantaneous voltage ¾ ω is the angular frequency; ω =2 π f f: frequency (Hz) ¾ SET YOUR CALCULATOR TO RADIANS WHERE NECESSARY I V(t)=V 0 sin ω t R I R (A) V 0 =10 V R=2 Ohm ω =1 rad/s
PHY232 - Remco Zegers - alternating currents and electromagnetic waves 5 lon-capa ¾ you should now do problem 1 from set 7.

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PHY232 - Remco Zegers - alternating currents and electromagnetic waves 6 rms currents/voltages ¾ To understand energy consumption by the circuit, it doesn’t matter what the sign of the current/voltage is. We need the absolute average currents and voltages (root-mean-square values) : ¾ V rms =V max / 2 ¾ I rms =I max / 2 ¾ The following hold: ¾ V rms =I rms R ¾ 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 ¾ We already saw (DC): ¾ P=VI=V 2 /R=I 2 R ¾ For AC circuits with a single resistor: ¾ P(t)=V(t)*I(t)=V 0 I 0 sin 2 ω t ¾ The average power consumption: ¾ P ave =V rms *I rms =V 2 rms /R=I 2 rms R ¾ 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)

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PHY232 - Remco Zegers - alternating currents and electromagnetic waves 8 vector representation time (s) V 0 -V 0 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). θ = ω t
PHY232 - Remco Zegers - alternating currents and electromagnetic waves 9 phasors I R (A) I(t) V(t) t θ = ω t The instantaneous current and voltage over R are the projections on the t-axis (horizontal axis) of vectors rotating with ang. frequency ω .

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AC and EM waves - alternating currents electromagnetic...

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