Physics 212 lectures 2425: RLC Circuits and AC Power

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Physics 212 lectures 24/25 RLC Circuits and AC
Power

• General AC Circuit Component Behavior
• Resistors, Capacitors, and Inductors all act to
  impede (like resist) current flow in an AC
  Circuit.
• The frequency of the sine wave current shape
  affects the amount of impedance (like
  resistance).

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• Resistors in AC Circuits
• Resistors in AC circuits act exactly the same as
  they do in DC circuits
• We can apply Ohms law or use the series/parallel
  combination rules just like we did for AC
  circuits

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• Capacitors in AC Circuits
• Positive current flow
• First, current flows onto (positive charge builds
  up) the capacitor.
• This builds up voltage on the capacitor that
  wants to push current back the other way.
• However, this happens while current is still
  being pushed onto the capacitor.
• Thus, the capacitor begins to resist the current
  flow.
• Negative current flow
• First, current flow out of (negative charge
  builds up) the capacitor.
• This builds up voltage on the capacitor that
  wants to pull the current back into it.
• However, this happens while current is still
  being pulled out of the capacitor.
• Thus, the capacitor begins to resist the current
  flow.
• So, we say that current leads voltage in a
  capacitor.

4

• Inductors in AC Circuits
• Inductors resist changes in current, and since
  the current keeps changing direction in an AC
  circuit, a voltage builds up across the inductor
  according the inductor equation for back EMF.

• Voltages (back EMFs) on inductors always oppose
  (or impede (resist)) the AC current.
• So, we say that voltage leads current in an
  inductor.

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• AC Resistance Equations (Impedance, or Reactance)

Resistors no change
Capacitors impedance dependant on frequency
Inductors impedance dependent on frequency
Total
Note The inductor and capacitor work to cancel
each other out. This is because one has voltage
leading current while the other has current
leading voltage.
Ohms Law in AC
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• Power in AC Circuits

• The power in an AC circuit works just like the
  power in DC circuits except that we use impedance
  rather than resistance, and we must use a phase
  angle factor since the current and resistance
  dont reach their peaks at the same time when
  capacitors and inductors are used.

or

• Maximum power can be delivered when the phase
  angle factor due to the capacitors and inductors
  is equal to 1.

• Resonant frequency
• Maximum power occurs at the resonant frequency,
  when XL and XC completely cancel each out (set
  XLXC and solve for f0).

or
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Example Ch 33 19 L400mH, C4.43uF, R500Ohm,
connected in series to 50Hz AC source with
Imax250mA. Find (a) Vmax (b) Find phase angle
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Example Ch 33 25Hand acts as 20pF capacitor
and 50kOhm resistor between secondary side of
transformer and ground as shown. Primary is 120V
at 60Hz. Find Vrms across hand.
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Example Ch 33 30RLC circuit has L50mH, R40
Ohms, C50uF, and Vrms100V and ?1000rad/s.
Find (a) current in circuit (b) power of source
(c) power delivered to resistor
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Example Ch 33 35Power P is transmitted over
distance d at voltage ?V with 1 loss. Assuming
uniform current density, find diameter of copper
wire required for circuit.