LECTURE 25 INDUCTANCE AND RL CIRCUITS
Instructor: Kazumi Tolich Lecture 25
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¨ Reading chapter 23.7 to 23.9. ¤ Inductance ¤ Energy stored in magnetic field ¤ RL circuits Quiz: 1
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¨ The current is flowing upward on the front side of the coil and is increasing as a function of time. Are there an induced emf and induced current in the coil? If so, what is the effect of the induced current? A. No. B. Yes. It acts to further increase the rate of change of the current. C. Yes. It acts to decrease the rate of change of current.
� Quiz: 25-1 answer
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¨ Yes. It acts to decrease the rate of change of current.
¨ The increasing current creates increasing magnetic field that points to the left inside the coil.
¨ Due to the change in magnetic flux through the coil, an emf is induced.
¨ According to Lez’s law, the induced emf acts to oppose the change of the magnetic flux through the coil.
� Self-inductance
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¨ Self-inductance, or Inductance, �, is the proportionality constant that tells us how much emf will ∆ be induced for a given rate of change in current: ℰ = � . ∆
∆Φ � = � ∆�
¨ An object designed to have a large inductance is called an inductor and is represented by the following symbol in a circuit diagram:
¨ The inductance depends only on the geometry.
¨ The inductance of a long solenoid with � turns of cross sectional area � and length ℓ is � = = � � �ℓ, where � = . ℓ ℓ Example: 1
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¨ A current I = 1.0 A passes through an inductor coil with L = 10.0 mH. What potential difference is induced across the coil if the current drops steadily to zero in Δt = 5.0 μs? Energy in magnetic field
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¨ It takes energy to establish a current in an inductor; this energy is stored in the inductor’s magnetic field.
¨ The energy stored in an inductor with an inductance � carrying a current � is given by
1 � = �� 2
¨ This energy is stored in the magnetic field. The energy density of magnetic field is
� � = 2� Example: 2
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¨ A solenoid with N = 2000 turns has a cross-sectional area equal to A = 4.0 × 10-4 m2 and a length equal to l = 0.30 m. The solenoid carries a current of I = 4.0 A. a) Calculate the magnetic energy stored in the solenoid. b) Find the magnetic energy density in the solenoid. RL circuit/Demo: 1
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¨ A circuit containing a resistor and an inductor is called an RL circuit. ¤ Current in a RL circuit cannot change discontinuously.
¨ The current in the circuit grows and approaches the final value after the switch is closed at � = 0.
ℰ � = 1 − � ⁄ �