- TL LR
(b)
L2
(a)
Fig. 4.31.
is R = 1.0 Q. At a certain moment the switch Sw was disconnected.
Find the energy of oscillations in the circuit
(a) immediately after the switch was disconnected;
(b) t = 0.30 s after the switch was disconnected.
4.110. Damped oscillations are induced in a circuit whose quality
factor is Q = 50 and natural oscillation frequency is vo = 5.5 kHz.
How soon will the energy stored in the circuit decrease ri = 2.0
times?
4.111. An oscillating circuit incorporates a leaking capacitor.
Its capacitance is equal to C and active resistance to R. The coil
inductance is L. The resistance of the coil and the wires is negligible.
Find:
(a) the damped oscillation frequency of such a circuit;
(b) its quality factor.
4.112. Find the quality factor of a circuit with capacitance C =
= 2.0 p,F and inductance L = 5.0 mH if the maintenance of undamped oscillations in the circuit with the voltage amplitude across the
capacitor being equal to Vm = 1.0 V requires a power (P)
0.10 mW. The damping of oscillations is sufficiently low.
4.113. What mean power should be fed to an oscillating circuit
with active resistance R = 0.45 52 to maintain undamped harmonic
oscillations with current amplitude /, = 30 mA?
4.114. An oscillating circuit consists of a capacitor with capacitance C = 1.2 nF and a coil with inductance L = 6.0 iLtli and
active resistance R = 0.50 SI. What mean power should be fed to
the circuit to maintain undamped harmonic oscillations with voltage amplitude across the capacitor being equal to Vm = 10 V?
4.115. Find the damped oscillation frequency of the circuit shown
in Fig. 4.30. The capacitance C, inductance L, and active resistance R
are supposed to be known. Find how must C, L, and R be interrelated to make oscillations possible.
~
tRC
Fig. 4.30.
4.116. There are two oscillating circuits (Fig. 4.31) with capacitors of equal capacitances. How must inductances and active resistances of the coils be interrelated for the frequencies and damping
of free oscillations in both circuits to be equal? The mutual inductance of coils in the left circuit is negligible.
4.117. A circuit consists of a capacitor with capacitance C and
a coil of inductance L connected in series, as well as a switch and a
resistance equal to the critical value for this circuit. With the switch
183
(b)
L2
(a)
Fig. 4.31.
is R = 1.0 Q. At a certain moment the switch Sw was disconnected.
Find the energy of oscillations in the circuit
(a) immediately after the switch was disconnected;
(b) t = 0.30 s after the switch was disconnected.
4.110. Damped oscillations are induced in a circuit whose quality
factor is Q = 50 and natural oscillation frequency is vo = 5.5 kHz.
How soon will the energy stored in the circuit decrease ri = 2.0
times?
4.111. An oscillating circuit incorporates a leaking capacitor.
Its capacitance is equal to C and active resistance to R. The coil
inductance is L. The resistance of the coil and the wires is negligible.
Find:
(a) the damped oscillation frequency of such a circuit;
(b) its quality factor.
4.112. Find the quality factor of a circuit with capacitance C =
= 2.0 p,F and inductance L = 5.0 mH if the maintenance of undamped oscillations in the circuit with the voltage amplitude across the
capacitor being equal to Vm = 1.0 V requires a power (P)
0.10 mW. The damping of oscillations is sufficiently low.
4.113. What mean power should be fed to an oscillating circuit
with active resistance R = 0.45 52 to maintain undamped harmonic
oscillations with current amplitude /, = 30 mA?
4.114. An oscillating circuit consists of a capacitor with capacitance C = 1.2 nF and a coil with inductance L = 6.0 iLtli and
active resistance R = 0.50 SI. What mean power should be fed to
the circuit to maintain undamped harmonic oscillations with voltage amplitude across the capacitor being equal to Vm = 10 V?
4.115. Find the damped oscillation frequency of the circuit shown
in Fig. 4.30. The capacitance C, inductance L, and active resistance R
are supposed to be known. Find how must C, L, and R be interrelated to make oscillations possible.
~
tRC
Fig. 4.30.
4.116. There are two oscillating circuits (Fig. 4.31) with capacitors of equal capacitances. How must inductances and active resistances of the coils be interrelated for the frequencies and damping
of free oscillations in both circuits to be equal? The mutual inductance of coils in the left circuit is negligible.
4.117. A circuit consists of a capacitor with capacitance C and
a coil of inductance L connected in series, as well as a switch and a
resistance equal to the critical value for this circuit. With the switch
183