The frequency of oscillation of a certain LC circuit is 200 kHz. At time t = 0, plate A

An oscillating LC circuit consists of a 75.0 mH inductor and a \(3.60 \mu \mathrm{F}\) capacitor. If the maximum charge on the capacitor is \(2.90 \mu \mathrm{C}\), what are (a) the total energy in the circuit and (b) the maximum current? Text Transcription: 3.60 mu mathrm F 2.90 mu mathrm C

In a certain oscillating LC circuit, the total energy is converted from electrical energy in the capacitor to magnetic energy in the inductor in \(1.50 \mu \mathrm{s}\). What are (a) the period of oscillation and (b) the frequency of oscillation? (c) How long after the magnetic energy is a maximum will it be a maximum again? Text Transcription: 1.50 mu mathrm s

What is the capacitance of an oscillating LC circuit if the maximum charge on the capacitor is \(1.60 \mu \mathrm{C}\) and the total energy is \(140 \mu \mathrm{J}\)? Text Transcription: 1.60 mu mathrm C 140 mu mathrm J

In an oscillating LC circuit, L = 1.10 mH and \(C=4.00 \mu \mathrm{F}\). The maximum charge on the capacitor is \(3.00 \mu \mathrm{C}\). Find the maximum current. Text Transcription: C=4.00 mu mathrm F 3.00 mu mathrm C

The energy in an oscillating LC circuit containing a 1.25 H inductor is \(5.70 \mu \mathrm{J}\). The maximum charge on the capacitor is \(175 \mu \mathrm{C}\). For a mechanical system with the same period, find the (a) mass, (b) spring constant, (c) maximum displacement, and (d) maximum speed. Text Transcription: 5.70 mu mathrm J 175 mu mathrm C

A single loop consists of inductors \(\left(L_{1}, L_{2}, \ldots\right)\), capacitors \(\left(C_{1},\right. \left.C_{2}, \ldots\right)\), and resistors \(\left(R_{1}, R_{2}, \ldots\right)\) connected in series as shown, for example, in Fig. 31-27a. Show that regardless of the sequence of these circuit elements in the loop, the behavior of this circuit is identical to that of the simple LC circuit shown in Fig. 31-27b. (Hint: Consider the loop rule and see Problem 47 in Chapter 30.) Text Transcription: (L_1, L_2, ldots) (C_1, C_2, ldots) (R_1, R_2, ldots)

In an oscillating LC circuit with L = 50 mH and \(C=4.0 \mu \mathrm{F}\), the current is initially a maximum. How long will it take before the capacitor is fully charged for the first time? Text Transcription: C=4.0 mu mathrm F

LC oscillators have been used in circuits connected to loudspeakers to create some of the sounds of electronic music. What inductance must be used with a \(6.7 \mu \mathrm{F}\) capacitor to produce a frequency of 10 kHz, which is near the middle of the audible range of frequencies? Text Transcription: 6.7 mu mathrm F

In an oscillating LC circuit, L = 3.00 mH and \(C=2.70 \mu \mathrm{F}\). At t = 0 the charge on the capacitor is zero and the current is 2.00 A. (a) What is the maximum charge that will appear on the capacitor? (b) At what earliest time t > 0 is the rate at which energy is stored in the capacitor greatest, and (c) what is that greatest rate? Text Transcription: C=2.70 mu mathrm F

To construct an oscillating LC system, you can choose from a 10 mH inductor, a \(5.0 \mu \mathrm{F}\) capacitor, and a \(2.0 \mu \mathrm{F}\) capacitor. What are the (a) smallest, (b) second smallest, (c) second largest, and (d) largest oscillation frequency that can be set up by these elements in various combinations? Text Transcription: 5.0 mu mathrm F 2.0 mu mathrm F

An inductor is connected across a capacitor whose capacitance can be varied by turning a knob. We wish to make the frequency of oscillation of this LC circuit vary linearly with the angle of rotation of the knob, going from \(2 \times 10^{5} \text { to } 4 \times 10^{5} \mathrm{Hz}\) as the knob turns through \(180^{\circ}\). If L = 1.0 mH, plot the required capacitance C as a function of the angle of rotation of the knob. Text Transcription: 2 times 10^5 to 4 times 10^5 mathrm Hz 180^circ

In Fig. 31-28, \(R= 14.0 \mathrm{s}, C=6.20 \mu \mathrm{F}\), and L = 54.0 mH, and the ideal battery has emf \(\mathscr{E}=34.0 \mathrm{V}\). The switch is kept at a for a long time and then thrown to position b. What are the (a) frequency and (b) current amplitude of the resulting oscillations? Text Transcription: R= 14.0 mathrm s, C=6.20 mu mathrm F mathscr E =34.0 mathrm V

In an oscillating LC circuit in which \(C=4.00 \mu \mathrm{F}\), the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 mA. What are (a) the inductance L and (b) the frequency of the oscillations? (c) How much time is required for the charge on the capacitor to rise from zero to its maximum value? Text Transcription: C=4.00 mu mathrm F

In an oscillating LC circuit with \(C=64.0 \mu \mathrm{F}\), the current is given by i = (1.60) sin(2500t + 0.680), where t is in seconds, i in amperes, and the phase constant in radians. (a) How soon after t = 0 will the current reach its maximum value? What are (b) the inductance L and (c) the total energy? Text Transcription: C=64.0 mu mathrm F

A series circuit containing inductance \(L_{1}\) and capacitance \(C_{1}\) oscillates at angular frequency \(\omega\). A second series circuit, containing inductance \(L_{1}\) and capacitance \(C_{1}\), oscillates at the same angular frequency. In terms of \(\omega\), what is the angular frequency of oscillation of a series circuit containing all four of these elements? Neglect resistance. (Hint: Use the formulas for equivalent capacitance and equivalent inductance; see Module 25-3 and Problem 47 in Chapter 30.) Text Transcription: L_1 C_1 omega L_1 C_1 omega

In an oscillating LC circuit, L = 25.0 mH and \(C=7.80 \mu \mathrm{F}\). At time t = 0 the current is 9.20 mA, the charge on the capacitor is \(3.80 \mu \mathrm{C}\), and the capacitor is charging. What are (a) the total energy in the circuit, (b) the maximum charge on the capacitor, and (c) the maximum current? (d) If the charge on the capacitor is given by \(q=Q \cos (\omega t+\phi)\), what is the phase angle \(\phi\)? (e) Suppose the data are the same, except that the capacitor is discharging at t = 0. What then is \(\phi\)? Text Transcription: C=7.80 mu mathrm F 3.80 mu mathrm C q=Q cos (omega t+phi) phi phi

The frequency of oscillation of a certain LC circuit is 200 kHz. At time t = 0, plate A of the capacitor has maximum positive charge. At what earliest time t > 0 will (a) plate A again have maximum positive charge, (b) the other plate of the capacitor have maximum positive charge, and (c) the inductor have maximum magnetic field?

A 0.50 kg body oscillates in SHM on a spring that, when extended 2.0 mm from its equilibrium position, has an 8.0 N restoring force. What are (a) the angular frequency of oscillation, (b) the period of oscillation, and (c) the capacitance of an LC circuit with the same period if L is 5.0 H?

A variable capacitor with a range from 10 to 365 pF is used with a coil to form a variable-frequency LC circuit to tune the input to a radio. (a) What is the ratio of maximum frequency to minimum frequency that can be obtained with such a capacitor? If this circuit is to obtain frequencies from 0.54 MHz to 1.60 MHz, the ratio computed in (a) is too large. By adding a capacitor in parallel to the variable capacitor, this range can be adjusted. To obtain the desired frequency range, (b) what capacitance should be added and (c) what inductance should the coil have?

In an oscillating LC circuit, when 75.0% of the total energy is stored in the inductor’s magnetic field, (a) what multiple of the maximum charge is on the capacitor and (b) what multiple of the maximum current is in the inductor?

An oscillating LC circuit consisting of a 1.0 nF capacitor and a 3.0 mH coil has a maximum voltage of 3.0 V. What are (a) the maximum charge on the capacitor, (b) the maximum current through the circuit, and (c) the maximum energy stored in the magnetic field of the coil?

An oscillating LC circuit has a current amplitude of 7.50 mA, a potential amplitude of 250 mV, and a capacitance of 220 nF. What are (a) the period of oscillation, (b) the maximum energy stored in the capacitor, (c) the maximum energy stored in the inductor, (d) the maximum rate at which the current changes, and (e) the maximum rate at which the inductor gains energy?

Using the loop rule, derive the differential equation for an LC circuit (Eq. 31-11).