Physics 202, Lecture 17 Today’s Topics Inductance (Ch 32) Reminder of Faraday’s and Lenz’s Laws Self Inductance Mutual Inductance Energy Stored in B Field RL CircuitsReview: Faraday’s Law of Induction Faraday’s Law in plain words: When the magnetic flux through an area is changed, an emf is produced along the closed path enclosing the area. Quantitatively: A B θ"conventional direction of ε"Note the - signReview: Lenz’s Law Lenz’s law in plain words: the induced emf always tends to work against the original cause of flux change Cause of dΦB/dt “Current” due to Induced ε will: Increasing B generate B in opposite dir. Decreasing B generate B in same dir. Relative motion subject to a force in opposite direction of relative motions The magnetic flux due to self inductance is proportional to I: The induced emf is proportional to dI/dt: When the current in a conducting device changes, an induced emf is produced in the opposite direction of the source current self inductance Self Inductance L: Inductance, unit: Henry (H)Exercise: Calculate Inductance of a Solenoid show that for an ideal solenoid: (see board) Reminder: magnetic field inside the solenoid (Ch 30) € L =µ0N2AlArea: A # of turns: NMutual Inductance For coupled coils: ε2 = - M12 dI1/dt ε1 = - M21 dI2/dt Can prove (not here): M12=M21=M M: mutual inductance (unit: also Henry) ε2 = - M dI1/dt ε1 = - M dI2/dtExamples of Coupled Coils (Transformers) !S!P=NSNPEnergy Stored in a Magnetic Field When an inductor of inductance L is carrying a current changing at a rate dI/dt, the power supplied is The work needed to increase the current in an inductor from zero to some value I U =!t0P dt =!I0LIdI =12LI2Energy in an Inductor Energy stored in an inductor is U= ½ LI2 This energy is stored in the form of magnetic field: energy density: uB = ½ B2/µ0 (recall: uE= ½ ε0E2) Compare: Inductor: energy stored U= ½ LI2 Capacitor: energy stored U= ½ C(ΔV)2 Resistor: no energy stored, (all energy converted to heat)Basic Circuit Components Component Symbol Behavior in circuit Ideal battery, emf ΔV=V+-V- =ε Resistor ΔV= -IR Realistic Battery (Ideal) wire ΔV=0 (R=0, L=0, C=0) Capacitor ΔV=V- - V+ = - q/C, dq/dt =I Inductor ΔV= - LdI/dt (Ideal) Switch L=0, C=0, R=0 (on), R=∞ (off) Transformer Future Topics Diodes, Transistors,… r ε" An inductor and are resistance constitute a RL circuit Any inductor has a resistance, R R could also include any other additional resistance When the current starts to flow a voltage drop will occur a the resistance and the inductance Once current stabilizes, reaches maximum of RL CircuitExercise: Turn on RL Circuit Apply Kirchhoff loop rule € I =V0R(1− e−tL / R)Exercise: Turn on RL Circuit (cont) Note: the time constant is τ=L/R Quiz: What is the current when t=∞ ? € I =V0R(1− e−tL / R)Exercise: Turn off RL Circuit Apply Kirchhoff loop rule € I = I0e−tL / RExercise: Turn off RL Circuit (cont) Note: the time constant is τ=L/R Quiz: What is the current when t=∞ ? € I = I0e−tL /
View Full Document
Unlocking...