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 Circuits Review 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 conventional direction of B Note the sign A Review 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 d B dt Current due to Induced 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 Self Inductance When the current in a conducting device changes an induced emf is produced in the opposite direction of the source current self inductance The magnetic flux due to self inductance is proportional to I The induced emf is proportional to dI dt L Inductance unit Henry H Exercise Calculate Inductance of a Solenoid show that for an ideal solenoid Area A 2 0 N A L l see board of turns N Reminder magnetic field inside the solenoid Ch 30 Mutual Inductance For coupled coils 2 M12 dI1 dt 1 M21 dI2 dt Can prove not here M12 M21 M M mutual inductance unit also Henry 2 M dI1 dt 1 M dI2 dt Examples of Coupled Coils Transformers S NS P NP Energy 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 0 t P dt 0 I 1 2 LIdI LI 2 Energy in an Inductor Energy stored in an inductor is U LI2 This energy is stored in the form of magnetic field energy density uB B2 0 recall uE 0E2 Compare Inductor energy stored U LI2 Capacitor energy stored U C V 2 Resistor no energy stored all energy converted to heat Basic Circuit Components Component Symbol Behavior in circuit Ideal battery emf V V V Resistor V IR r Realistic Battery Ideal wire Capacitor Inductor Ideal Switch Transformer Diodes Transistors V 0 R 0 L 0 C 0 V V V q C dq dt I V LdI dt L 0 C 0 R 0 on R off Future Topics RL Circuit 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 Exercise Turn on RL Circuit Apply Kirchhoff loop rule V0 I 1 e R t L R Exercise Turn on RL Circuit cont V0 I 1 e R t L R Note the time constant is L R Quiz What is the current when t Exercise Turn off RL Circuit Apply Kirchhoff loop rule I I0e t L R Exercise Turn off RL Circuit cont I I0e t L R Note the time constant is L R Quiz What is the current when t
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