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Lecture 21 preview mar25

# Lecture 21 preview mar25 - Lecture 21 LR LC and LRC...

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Lecture 21: LR, LC, and LRC circuits Finish Ch 30 today Thursday: begin AC circuits, Ch 31 Exam next week through Thursday’s material

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Energy stored in “charging” an inductor L in stored energy U LI Lidi Pdt W low is i when low dt di iL i P I ext ext = = = = = = 2 0 2 1 ) ( ξ If we increase current from 0 to I in an inductor work must be done against the opposing emf, ξ = -Ldi/dt. This is similar to charging a battery. The power required of some external emf is: We say U is stored in the B field SOLENOID: 0 2 2 0 0 2 2 0 2 2 1 2 1 μ μ μ μ B Al U u density B Al U l NI B and I l A N U sol B sol sol sol = = = = = Energy Density, u B compare with u E =(1/2)ε 0 E 2
Inductors in circuits (we have R and C, now we add L) i increasing ξ + - ΔV in direction of I is negative ΔV = -Ldi/dt i decreasing ξ - + ΔV in direction of I is positive ΔV = -Ldi/dt So, in the direction of current ΔV = -Ldi/dt. Let’s use Kirchhoff’s loop rule

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Current buildup in the LR circuit (take a walk around Kirchhoff’s loop) ξ ξ = + = - - iR dt di L
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