IPhO 1983 Theoretical Questions
2.Electricity – Problem II (8 points)
Different kind of oscillation
Let’s consider the electric circuit in the figure, for whichL 10 mH ,
1
L 20mH, C 10 nF, C 5 nF andR 100k. The switch K
2 1 2
being closed the circuit is coupled with a source of alternating current. The
current furnished by the source has constant intensity while the frequency of
the current may be varied.
a. Find the ratio of frequency f for which the active power in circuit
m
has the maximum value P and the frequency difference
m
f f f of the frequencies f and f for which the active
power in the circuit is half of the maximum powerP .
m
The switch K is now open. In the moment t immediately after the switch
0
is open the intensities of the currents in the coils L and i 0,1 A and
1 01
i 0,2 A L (the currents flow as in the figure); at the same
02 1
moment, the potential difference on the capacitor with capacity C is
1
u 40V :
0
b. Calculate the frequency of electromagnetic oscillation in
LC C L circuit;
1 1 2 2
c. Determine the intensity of the electric current in the AB
conductor;
d. Calculate the amplitude of the oscillation of the intensity of
electric current in the coilL .
1
Neglect the mutual induction of the coils, and the electric resistance of
the conductors. Neglect the fast transition phenomena occurring when
the switch is closed or opened.
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