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RL Circuit

RL Circuit. Switch to position a. t=0, i=0. t= R/L. Initially, i change is max, thus largest V L . After t>> t, all voltage is on R, di/dt=0, so V L =0. In a dc circuit, inductor behaves like a short circuit. Switch to position b. Dissipated power. Power supplied by battery.

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RL Circuit

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

  2. Dissipated power Power supplied by battery Work stored 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 Inductor Capacitor Current (iL) must be continuous, i.e. i+=i- Voltage (Vc) must be continous, i.e. V+=V- At t>>t Open circuit Short circuit Magnetic field energy stored in an inductor:

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

  4. LC Circuit • Charged C connected L Vmax=qmax/C, i = 0, di/dt: max UE=qmax2/2C, max UB=Li2/2=0 b) U=UB+UE c) imax, q=0, UB max

  5. LC oscillation Vmax=qmax/C, i=0 Vmax=qmax/C, i=0 UE=qmax2/2C, max UB=Li2/2=0 UE=qmax2/2C, max UB=Li2/2=0 The charge starts to flow back the other way, resulting opposite current UE=q2/2C, UB=Li2/2 q=0, imax UE=q2/2C=0 UB=Limax2/2, max Speed of charging depends on L, C

  6. LC oscillation

  7. LC oscillation The oscillations continuous indefinitely in the absence of loss (R=0) The Vc (or charges) is out of phase with i, i.e. Vc max. at i=0, vice versa.  Oscillating block-spring systems LC circuit q Displacement: x i=dq/dt v=dx/dt m L 1/k C UB=Li2/2 Uk=mv2/2 UE=q2/2C U=kx2/2

  8. LC oscillation Circuit

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

  10. Example: RC circuit 33-19P, In an oscillating LC circuit, L=3.0 mH and C=2.60 mF. 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?

  11. Damped and Forced Oscillations Damped Oscillation Forced Oscillation

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