Physics 212 Lecture 22: Mutual Inductance, LC Circuits, and RLC Circuits

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Physics 212 Lecture 22 Mutual Inductance, LC
Circuits, and RLC Circuits

• Mutual Inductance (M)
• Process
• Change in current flow in loop 1
• Magnetic field produced by loop 1 due to current
  flow
• Magnetic Field from loop 1 passes through loop 2
• Change in magnetic flux through loop 2 produces
  voltage
• Current flows in loop 2
• Meaning
• Electromagnetic changes in one coil are noticed
  in nearby coils
• Use
• Transformers
• One coil has more turns than the other
• Voltage in coils in proportional to number of
  turns

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Mutual Inductance Equations
Diagram
Mutual inductance calculation for two coils
Induced Voltage calculation for two coils
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LC Circuits (Energy Analysis)

• Obtain differential equation for charge on
  capacitor as a function of time
• Charge oscillates between
• collecting on capacitor
• flowing through inductor

Diagram
Energy Stored
Rate of Change of Energy Stored
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LC Circuits (Current or Charge Oscillations)
charge
current
Results from solution of differential equation
Note frequency of oscillation
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RLC Circuits
Diagram
Resistor will cause oscillations to damp out
This result can be derived from an energy
analysis similar to LC circuits
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Example Ch 32 43Two solenoids overlap and
share same axis. A has N400 with I3.5A to
produce flux of 300uWb. A causes flux of 90uWb
in B and B has N700.(a) Find M (b)
Find L for A(c) Find EMF in B if current in
A now increases at 0.5A./s.
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Example Ch 32 52See Figure. Switch is
connected to a for long time before moving to
b. Find (a) f for circuit (b)Qmax on
capacitor (c) Imax in inductor (d) Utotal in
circuit at t3s.