Irodov Solutions → Oscillations and waves → Electric Oscillations 
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 V_{m} and then at the moment t = 0 the switch was closed. Find:
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 C_{1} = 2.0 μF and C_{2} = 3.0 μF. The capacitors were charged to a voltage V = 180 V, and then the switch Sw was closed. Find:
4.103. A circuit with capacitance C and inductance L generates free damped oscillations with current varying with time as I = I_{m}e^{βt}sin ωt. Find the voltage across the capacitor as a function of time, and in particular, at the moment t = 0.
4.104. An oscillating circuit consists of a capacitor with capacitance C = 4.0 μF and a coil with inductance L = 2.0 mH and active resistance R = 10 Ω. Find the ratio of the energy of the coil's magnetic field to that of the capacitor's electric field at the moment when the current has the maximum value.
4.107. An oscillating circuit consists of capacitance C = 10 μF, inductance L = 25 mH, and active resistance R = 1.0 Ω. How many oscillation periods does it take for the current amplitude to decrease efold?
4.108. How much (in per cent) does the free oscillation frequency ω of a circuit with quality factor Q = 5.0 differ from the natural oscillation frequency ω_{0} of that circuit?
4.109. In a circuit shown in Fig. 4.29 the battery emf is equal to ξ = 2.0 V, its internal resistance is r = 9.0 Ω, the capacitance of the capacitor is C = 10 μF, the coil inductance is L = 100 mH, and the resistance is R = 1.0 Ω. At a certain moment the switch Sw was disconnected. Find the energy of oscillations in the circuit
4.110. Damped oscillations are induced in a circuit whose quality factor is Q = 50 and natural oscillation frequency is ν_{0} = 5.5 kHz. How soon will the energy stored in the circuit decrease η = 2.0 times?
4.119. A circuit consisting of a capacitor with capacitance C and a resistance R connected in series was connected at the moment t = 0 to a source of ac voltage V = V_{m} cos ωt. Find the current in the circuit as a function of time t.
4.121. A circuit consisting of a capacitor and an active resistance R = 110 Ω connected in series is fed an alternating voltage with amplitude V_{m} = 110 V. In this case the amplitude of steadystate current is equal to I_{m} = 0.50 A. Find the phase difference between the current and the voltage fed.
4.122. Fig. 4.32 illustrates the simplest ripple filter. A voltage V = V_{0}(1 + cos ωt) is fed to the left input. Find:
4.136. A solenoid with inductance L = 7 mH and active resistance R = 44 Ω is first connected to a source of direct voltage V_{0} and then to a source of sinusoidal voltage with effective value V = V_{0}. At what frequency of the oscillator will the power consumed by the solenoid be η = 5.0 times less than in the former case?
4.138. A coil with inductance L = 0.70 H and active resistance r = 20 Ω is connected in series with an inductancefree resistance R. An alternating voltage with effective value V = 220 V and frequency ω = 314 s^{1} is applied across the terminals of this circuit. At what value of the resistance R will the maximum heat power be generated in the circuit? What is it equal to?
4.147. A circuit consists of a capacitor with capacitance C and a coil with active resistance R and inductance L connected in parallel. Find the impedance of the circuit at frequency ω of alternating voltage.
