Đề IPHO(vật lí quốc tế) 1983-3

IPhO 1983 Theoretical Question II MARKING SCHEME FOR ANSWERS TO THE THEORETICAL QUESTION II MARKING SCHEME – DIFFERENT KIND OF OSCILLATION Page 1 from 3 IPhO 1983 Theoretical Question II MARKING SCHEME – DIFFERENT KIND OF OSCILLATION Page 2 from 3 Part MARKING SCHEME - THE THEORETICAL QUESTION II - DIFFERENT KIND OF OSCILLATION Total Score s II.a. For:      + = += 21 21 21 LL LL L CCC 0.2p the impedance Z of the circuit Y L C R ZZ 1 11 1 22 =       ⋅ −⋅+       == ω ω 0.2p ( ) ( ) tIti ⋅⋅⋅= ω sin2 0.2p ( ) ( ) ϕω +⋅⋅⋅= tUtu sin2 0.2p R IZ R U P 222 ⋅ == 0.1p the maximal active power is realized for the maximum value of the impedance that is the minimal value of the admittance R Y 1 min = . 0.2p 2 IRP m ⋅= 0.2p LC f m ⋅⋅ = π 2 1 0.2p m PP 2 1 = 0.1p 2 22 2 1 IR R IZ ⋅= ⋅ 0.1p 0 11 2 = ⋅ − ⋅ ± CLCR ωω 0.2p the pulsation of the current ensuring an active power at half of the maximum power                    ⋅ − ⋅ +       ⋅ =           ⋅ + ⋅ +       ⋅ = − + CRCLCR f CRCLCR f 2 141 2 1 2 1 2 141 2 1 2 1 2 2 π π 0.2p the bandwidth of the circuit CR fff ⋅ =−=∆ −+ 1 2 1 π 0.1p ( ) ( )        ⋅ +⋅+ = ∆ = ∆ 21 2121 LL LLCC R f f L C R f f m m 0.2p final result: 150 = ∆ f f m 0.1p 2.5 points II.b. 2.2 points IPhO 1983 Theoretical Question II Professor Delia DAVIDESCU, National Department of Evaluation and Examination– Ministry of Education and Research- Bucharest, Romania Professor Adrian S.DAFINEI,PhD, Faculty of Physics – University of Bucharest, Romania MARKING SCHEME – DIFFERENT KIND OF OSCILLATION Page 3 from 3