Physics 212 lecture 26: RLC Circuit Resonance and Transformers

1
Physics 212 lecture 26 RLC Circuit Resonance
and Transformers

• Current and Power dependence on frequency
• Maximum power occurs at the resonant frequency,
  when XL and XC completely cancel each out (set
  XLXC and solve for f0), such that the phase
  angle 1.
• Maximum power occurs at maximum current.
• The frequency for maximum power is called the
  resonant frequency.

irms and P both functions of ? both peak at
2

• Current and Power Graphical relationship to
  frequency

• Full Width Half Maximum (FWHM)
• Take derivative dPav/d? 0 to find ?0 at Pmax
• Find Pav/max using ?0 from step 1.
• Find Pav/max/2 and solve for ? (get two values)
• Find ??
• Circuit Q values (Tunability)
• High Q, small R fine tuning circuit with narrow
  resonance
• Low Q, high R poorly tunable circuit with wide
  resonance

Result
3

• Transformers Setup
• Transformers are simply AC voltage changers
• Transformers work by winding two different wires
  around an iron core different numbers of times.
• Primary side windings (N1) incoming voltage
  (V1)
• Secondary side windings (N2) outgoing voltage
  (V2)
• Step-up transformers increase voltage, Step-down
  transformers decrease voltage

Diagram
4
Transformers Equations
Apply Faradays law to each set of windings
Primary
Secondary
Recognize rate of change of flux is equal for
each winding
If flux remains in core, no energy is lost
between sides
?, power delivered is equal on both sides for
ideal transformers
Typical real transformers are 90-99 efficient
5
Example Ch 33 38 LC circuit AM radio tuner
has L0.2mH and variable C to give resonance
between 550kHz and 1650kHz. Find required range
in C.
6
Example Ch 33 48Furnace ignition has 90
efficient transformer with Vs10kV and Vp120V
rms. Impedance on primary is 24 Ohm. Find (a)
required turns ratio (b) current in secondary (c)
impedance in secondary