Presentation on theme: "Lectures (Ch. 30) Inductance and Self-inductunce"— Presentation transcript:
1 Lectures 18-19 (Ch. 30) Inductance and Self-inductunce Mutual inductunceTesla coilInductors and self-inductanceToroid and long solenoidInductors in series and parallelEnergy stored in the inductor,energy density7. LR circuit8. LC circuit9. LCR circuit
2 Mutual inductanceVirce verse: if current in coil 2 is changing, the changing flux through coil 1 induces emf in coil 1.
3 Units of MJoseph Henry ( )Typical magnitudes: 1μH-1mH
12 Magnetic energy density Let’s consider a thin toroidal solenoid, but the result turns out to be correct for a general caseCompare to:Energy is stored in E inside the capacitorEnergy is stored in B inside the inductor
13 Example. Find U of a toroidal solenoid with rectangular area
23 Energy conservation law UC+UL=constUCULULUCtQ-QqT/2
24 Example. In LC circuit C=0.4 mF, L=0.09H. The initial charge on the capacitor is 0.005mC and the initial current is zero. Find: (a) Maximum charge in the capacitor (b) Maximum energy stored in the inductor; (c) the charge at the moment t=T/4, where T is a period of oscillations.
25 Example. In LC circuit C=250 ϻF, L=60mH. The initial current is 1.55 mA and the initial charge is zero. 1) Find the maximum voltage across the capacitor . At which moment of time (closest to an initial moment) it is reached? 2) What is a voltage across an inductor when a charge on the capacitor is 1 ϻ C?q
26 Example. In LC circuit C=18 ϻF, two inductors are placed in parallel: L1=L2=1.5H and mutual inductance is negligible.The initial charge on the capacitor is 0.4mC and the initial current through the capacitor is 0.2A. Find: (a) the current in each inductor at the instant t=3π/ω, where ω is an eigen frequency of oscillations; (b) what is the charge at the same instant? (c) the maximum energy stored in the capacitor;(d) the charge on the capacitor when the current in each inductor is changing at a rate of 3.4 A/s.
28 a) Underdamped oscillations: b) Critically damped oscillations:c) Overdamped oscillations:
29 Example. The capacitor is initially uncharged Example. The capacitor is initially uncharged. The switch starts in the open position and is then flipped to position 1 for 0.5s. It is then flipped to position 2 and left there. 1) What is a current through the coil at the moment t=0.5s (i.e. just before the switch was flipped to position 2)? 2) If the resistance is very small, how much electrical energy will be dissipated in it? 3) Sketch a graph showing the reading of the ammeter as a function of time after the switch is in position 2, assuming that r is small.10µF25Ω1250Vr10mHA3)
30 Induced oscillations in LRC circuit, resonance ~QAt the resonance condition: an amplitude greatly insreases