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
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IPhO 1983
Theoretical Question II
MARKING SCHEME – DIFFERENT KIND OF OSCILLATION
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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
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