IPhO 1983Theoretical Question II MARKING SCHEME FOR ANSWERS TO THE THEORETICAL QUESTION II... IPhO 1983Theoretical Question II Professor Delia DAVIDESCU, National Department of Evaluatio
Trang 1IPhO 1983
Theoretical Question II
MARKING SCHEME FOR ANSWERS TO THE THEORETICAL
QUESTION II
Trang 2IPhO 1983
Theoretical Question II
-DIFFERENT KIND OF OSCILLATION
Total Score s
+
=
+
=
2 1
2 1
2 1
L L
L L L
C C C
0.2p
the impedance Z of the circuit Y
L
C R
Z
1 1
1
2
⋅
−
⋅ +
=
=
ω
ω 0.2p ( )t I ( t)
i = ⋅ 2 ⋅ sin ω ⋅ 0.2p
( )t =U⋅ ⋅ (ω ⋅t+ ϕ)
u 2 sin 0.2p
R
I Z R
U P
2 2
2 = ⋅
= 0.1p
the maximal active power is realized for the maximum value of the impedance that is the minimal
value of the admittance
R
Ymin = 1 0.2p
2
I R
P m = ⋅ 0.2p
L C
f m
⋅
⋅
=
π
2
1 0.2p
m P P
2
1
= 0.1p
2 2
2
2
1
I R R
I Z
⋅
=
⋅ 0.1p
0 1 1
⋅
−
⋅
±
C L C
ω 0.2p the pulsation of the current ensuring an active power at half of the maximum power
⋅
−
⋅ +
⋅
=
⋅
+
⋅ +
⋅
=
−
+
C R C L C R f
C R C L C R f
2
1 4
1 2
1 2 1
2
1 4
1 2
1 2 1
2 2
π
π
0.2p
the bandwidth of the circuit
C R f
f f
⋅
=
−
=
2
1
π 0.1p
⋅
+
⋅ +
=
∆
=
∆
2 1
2 1 2 1
L L
L L C C R f f
L
C R f f
m
m
0.2p
final result: =150
∆f
f m
0.1p
2.5 points
points
Trang 3IPhO 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