4.94. Due to a certain cause the free electrons in a plane copper
plate shifted over a small distance x at right angles to its surface.
As a result, a surface charge and a corresponding restoring force
emerged, giving rise to so-called plasma oscillations. Find the
angular frequency of these oscillations if the free electron concentration in copper is n, = 0.85.1029 m-1.
4.95. An oscillating circuit consisting of a capacitor with capacitance C and a coil of inductance L maintains free undamped oscillations with voltage amplitude across the capacitor equal to Vm.
For an arbitrary moment of time find the relation between the current I in the circuit and the voltage V across the capacitor. Solve
this problem using Ohm's law and then the energy conservation law.
4.96. An oscillating circuit consists of a capacitor with capacitance C, a coil of inductance L with negligible resistance, and a
switch. With the switch disconnected, the capacitor was charged to
a voltage Vff, and then at the moment t = 0 the switch was closed.
Find:
(a) the current I (t) in the circuit as a function of time;
(b) the emf of self-inductance in the coil at the moments when the
electric energy of the capacitor is equal to that of the current in the
coil.
4.97. In an oscillating circuit consisting of a parallel-plate capacitor and an inductance coil with negligible active resistance the
oscillations with energy W are sustained. The capacitor plates were
slowly drawn apart to increase the oscillation frequency i-fold.
What work was done in the process?
4.98. In an oscillating circuit shown in Fig. 4.27 the coil inductance
is equal to L = 2.5 mH and the capacitor have capacitances C1
2.0 p,F and C2 = 3.0 11,F. The capacitors were charged to a voltage
V = 180 V, and then the switch Sw was closed. Find:
(a) the natural oscillation frequency;
(b) the peak value of the current flowing through the coil.
L
C — C —
2
Sw
Fig. 4.27.
Fig. 4.28.
4.99. An electric circuit shown in Fig. 4.28 has a negligibly small
active resistance. The left-hand capacitor was charged to a voltage V0
and then at the moment t = 0 the switch Sw was closed. Find the
time dependence of the voltages in left and right capacitors.
4.100. An oscillating circuit consists of an inductance coil L and
a capacitor with capacitance C. The resistance of the coil and the lead
181
plate shifted over a small distance x at right angles to its surface.
As a result, a surface charge and a corresponding restoring force
emerged, giving rise to so-called plasma oscillations. Find the
angular frequency of these oscillations if the free electron concentration in copper is n, = 0.85.1029 m-1.
4.95. An oscillating circuit consisting of a capacitor with capacitance C and a coil of inductance L maintains free undamped oscillations with voltage amplitude across the capacitor equal to Vm.
For an arbitrary moment of time find the relation between the current I in the circuit and the voltage V across the capacitor. Solve
this problem using Ohm's law and then the energy conservation law.
4.96. An oscillating circuit consists of a capacitor with capacitance C, a coil of inductance L with negligible resistance, and a
switch. With the switch disconnected, the capacitor was charged to
a voltage Vff, and then at the moment t = 0 the switch was closed.
Find:
(a) the current I (t) in the circuit as a function of time;
(b) the emf of self-inductance in the coil at the moments when the
electric energy of the capacitor is equal to that of the current in the
coil.
4.97. In an oscillating circuit consisting of a parallel-plate capacitor and an inductance coil with negligible active resistance the
oscillations with energy W are sustained. The capacitor plates were
slowly drawn apart to increase the oscillation frequency i-fold.
What work was done in the process?
4.98. In an oscillating circuit shown in Fig. 4.27 the coil inductance
is equal to L = 2.5 mH and the capacitor have capacitances C1
2.0 p,F and C2 = 3.0 11,F. The capacitors were charged to a voltage
V = 180 V, and then the switch Sw was closed. Find:
(a) the natural oscillation frequency;
(b) the peak value of the current flowing through the coil.
L
C — C —
2
Sw
Fig. 4.27.
Fig. 4.28.
4.99. An electric circuit shown in Fig. 4.28 has a negligibly small
active resistance. The left-hand capacitor was charged to a voltage V0
and then at the moment t = 0 the switch Sw was closed. Find the
time dependence of the voltages in left and right capacitors.
4.100. An oscillating circuit consists of an inductance coil L and
a capacitor with capacitance C. The resistance of the coil and the lead
181