RL Circuit t=0, i=0  R/L Switch to position a Switch to position b Initially, i change is max, thus largest V L. After t>>  all voltage is on R, di/dt=0, so V L =0 In a dc circuit, inductor behaves like a short circuit

Inductor & Capacitor in DC Circuit If there is a sudden change in current or Voltage occurs in a circuit such as close or open a switch, then InductorCapacitor Current (i L ) must be continuous, i.e. i + =i - Voltage (V c ) must be continous, i.e. V + =V - At t>>  Short circuit Open circuit Magnetic field energy stored in an inductor: Power supplied by battery Dissipated power Work stored

Concept Check A battery is connected to a solenoid. When the switch is opened, the light bulb 1.Remain off 2.Goes off 3.Slowly dims out 4.Keeps burning as brightly as it did before the switch was opened. 5.Flares up brightly, then dims and goes out Answer 5

LC Circuit a)Charged C connected L V max =q max /C, i = 0, di/dt: max U E =q max 2 /2C, max U B =Li 2 /2=0 b) U=U B +U E c) i max, q=0, U B max

LC oscillation V max =q max /C, i=0 U E =q max 2 /2C, max U B =Li 2 /2=0 Speed of charging depends on L, C U E =q 2 /2C, U B =Li 2 /2 q=0, i max U E =q 2 /2C=0 U B =Li max 2 /2, max V max =q max /C, i=0 U E =q max 2 /2C, max U B =Li 2 /2=0 The charge starts to flow back the other way, resulting opposite current

LC oscillation

The oscillations continuous indefinitely in the absence of loss (R=0) The V c (or charges) is out of phase with i, i.e. V c max. at i=0, vice versa. LC circuit  Oscillating block-spring systems q Displacement: x i=dq/dtv=dx/dt L m C 1/k U B =Li 2 /2U k =mv 2 /2 U E =q 2 /2CU=kx 2 /2

LC oscillation Circuit

Concept Check Which Circuit takes the least time to fully discharge the capacitors during the oscillation (a) Answer: (b) has smaller C eq, thus smaller T, fast discharge (b)

Example: RC circuit 33-19P, In an oscillating LC circuit, L=3.0 mH and C=2.60  F. At t=0 the charge on the capacitor is zero and the current is 2.00 A. (a) what is the maximum charge that will appear on the capacitor? (b) In terms of the period T of the oscillation, how much time will elapse after t=0 until the energy stored in the capacitor will be increasing at its greatest rate? c) What is this greatest rate at which energy is transferred to the capacitor?

Damped and Forced Oscillations Damped OscillationForced Oscillation