Lesson 10

SELF-INDUCTANCE

• Closing a switch triggers a change in magnetic flux through the circuit.
• Resulting induced current:
  • It is not two separate currents.
  • Induced emf opposes the change in current (similar to back emf).

INDUCED EMF

• Key relationships:
  • Induced emf is proportional to the rate of change of magnetic flux.
  • Magnetic flux relates to the current in the circuit.
  • According to Lenz's Law:
  • The induced emf opposes the change in flux.
• Understanding components:
  • Resistance: opposition to current.
  • Inductance: opposition to changes in current.

CALCULATING INDUCTANCE

• Inductance, like resistance or capacitance, depends on circuit geometry.
• Formula for inductance:
  • $1H = \frac{Tm^2}{A}$
  • SI Unit: Henry [H]

EXAMPLES

Example 1

• (Details not provided)

Example 2

• A solenoid with:
  • 300 turns
  • Length = 25.0 cm
  • Cross-sectional area = 4.00 cm²
• Calculate self-induced emf with a rate of current decrease of 50.0 A/s.

RL CIRCUITS

• Analyzing circuits with inductors:
  • Focus on inductors for inductance calculations.
• Using Kirchhoff’s loop rule to analyze circuit behavior.

EXAMPLE PROBLEM

• Solenoid specifics:
  • 500 turns
  • Radius = 2 cm
  • Length = 15 cm
• Given a 3 A current, calculate time to decrease to 1 mA with a resistance of 10 ohms.

ENERGY STORED IN AN INDUCTOR

• Focus on potential differences in circuits after switch activation.

LC CIRCUITS

• Principles:
  • In ideal cases, oscillations can theoretically continue indefinitely if there is no resistance.
• Oscillations are described with:
  • Capacitor charge: $Q(t) = Q_0 \cos(\omega t)$
  • Inductor current: $I(t) = -\omega Q_0 \sin(\omega t)$

SIMPLE HARMONIC MOTION

• Natural frequency:
  • Frequency at which a system resonates.
  • Resonance amplifies oscillation amplitude when driven by matching frequency.

LC CIRCUITS EXAMPLE

• Tuning a radio to 920 kHz:
  • Given a 1.0 mH inductor, determine the required capacitance for tuning.