Electricity & Magnetism Lecture 20: Understanding Phasors and Reactance in AC Circuits, Schemes and Mind Maps of Physics

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➢ Driven AC Circuits ➢ Phase of V and I ▪ Conceputally ▪ Mathematically ▪ With phasors

Physics 2112

Unit 20

Outline:

it just got real this stuff is confusing the relationships between the capacitors, inductors, and resistors voltage This was the first somewhat challenging prelecture. I much prefer doing prelectures over reading a book. Please keep using this style next semester. Examples of the math on this, please! When the phi=0, what is happening- life is simple? Is the current across each element the same at a given instant? PHASORS!!!!!!!!!!!!!!! I don't understand reactance. what phasor diagrams do and how do we know if the current is out of phase with the capacitor? I don't understand why the voltage and current start where they do in the phaser diagrams. Would like to see examples in class per usual what is the relationship of the phase of current and voltage? Or between the voltage of the resistor and the inductor?

Your Comments

Unit 19, Slide 4 V L V R V C I

AC Generator e = V max sin( w d t ) Driving frequency = natural frequency (w o )

Capacitors C → I = V max w C cos( w t ) where XC = 1/ w C is like the “resistance” of the capacitor XC depends on w Amplitude = Vmax / XC Q = CV = CV max sin( w t ) 90 o Unit 20, Slide 7 wd frequency of signal generator (not wo)

Inductors L where XL = w L is like the “resistance” of the inductor XL depends on w 90 o sin( ) max V V t dt dI L L

= = w

cos( ) max t L V

I w

w

= − Amplitude = Vmax / XL

Question

Does the current “lead” or “lag” the voltage in the above plots? A. the current leads the voltage B. the current lags the voltage C. they are in phase These might be the current and voltage plots for a: A. capacitor B. inductor C. resistor

What does this look like together?

Notice phase relationships Green – inductor voltage Blue – capacitor voltage Red – resistor voltage Black – current

What about current?

Current is always the same through all elements (in series) Current and Voltage in phase across Resistor Current and voltage out of phase by unknown phase angle across signal generator (We’ll find this “phase angle” later.) Green – inductor voltage Blue – capacitor voltage Red – resistor voltage Black – current

Question

The potential difference across a single inductor is determined by a sinusoidal signal with amplitude of 5V and a frequency of 60Hz. The maximum current through the inductor is I max

. If I double the frequency of the potential signal to 120Hz, what with the value of the maximum current be? A. I max

B. I

max

C. No change (I max

D. 2*I

max E. 4*I max Unit 20, Slide 16

Reactance Summary L

R

R C X C

w

1

C

X L w

L

w goes up, 

c goes down Doesn’t depend on w

w goes up, 

L goes up

Example 20.1 (Resistor Resistance) L A 60Hz signal with a V max = 5V is sent through a 100W resistor. What is the maximum current, I max , through the resistor?

Think of same material graphically using “phasors” Phasors Phasor just thinks of sine wave as rotating vector

Imax XL Imax XC Imax R V L and V C 180 o out of phase Circuit using Phasors Represent voltage drops across elements as rotating vectors (phasors) V L and V R 90 o out of phase Remember V R and I in phase