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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

Power supplied by battery

Work stored

Inductor & Capacitor in DC CircuitIf 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:

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

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

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

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

(a)

Concept CheckWhich Circuit takes the least time to fully discharge the capacitors during the oscillation

Answer: (b) has smaller Ceq, thus smaller T, fast discharge

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?

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