Problem 5 A capacitor C is connected to an inductor L in a closed loopcircuit. Initially the capacitor has a charge Qo, and the current is zero. Themodified Krchoff loop rule for this circuit is18L.dt(a) Rewrite this equation in terms of charge only, by expressing the currentIn terms of the rate of change of the charge on the capacitor. Show that thecharge obeys the following equation:d²2Q1Q = 0.LCdt2(b) This is 280morphnc to the equation for a mass m connected to a springwith stiffness constant k, moving along the x axis+.dt²0,except that charge Q plays the role of the displacement r. Recall that a massconnected to a spring oscillates, with a natural frequency wo =comparison, if L = 1 mH, and C =oscillation of this LC series circuit?VElm. By10 µF, what is the natural frequeney of (c) The solution to the equation in (a) is Q(t) = Qo cos (wot). If L = 1mH, and C = 10 µF, and Qothe inductor? What is the maximum voltage across the capacitor? How is thevoltage across the capacitor related to the voltage across the inductor?= 1.0 mC, what is the maximum voltage across

Given, -QC=LdIdt Now, dIdt+QLC=0or d2Qdt2+1LCQ=0 (Since, I=dQdt)

Answered: Problem 5: A capacitor C is connected…

Similar questions

Students who are studying LR circuits obtain some identical inductors with a common inductance value L0 and some identical resistors with a common resistance value R0. They assemble a circuit with one inductor and one resistor in series with a voltage source and a simple switch, as shown. They close the switch, collect data, and observe that the time constant of the circuit has the value τ0.
The charge on the capacitor of an LC circuit with inductance L and capacitance C obeys the following expression. Find the maximum current in the circuit. q=Q cos [t/(LC)0.5] zero Q(LC) ⁰.5 Olmax/(LC)0.5 Imax QLC Q/(LC) 0.5
A loop of wire has a self-inductance of 5.5 mH. You pass a current of 9.0 Amps though the loop, and then drop the current to 0 at a contastant rate over 3.5 seconds. What is the EMF generated?
In a home stereo system, low sound frequencies are handled by large “woofer” speakers, and high frequencies by smaller “tweeter” speakers. For the best sound reproduction, low-frequency currents from the amplifier should not reach the tweeter. One way to do this is to place a capacitor in series with the 8.0 Ω resistance of the tweeter; one then has an RLC circuit with no inductor L (that is, an RLC circuit with L = 0). What value of C should be chosen so that the current through the tweeter at 200 Hz is half its value at very high frequencies?
In the analogy between an RLC circuit and a mass on a spring moving through a viscous fluid, which element in the RLC circuit represents the spring? O the resistor O the capacitor O the inductor O the power supply
The charge on the capacitor of an LC circuit with capacitance C and inductance L obeys the following equation. Find the maximum current in the circuit. q= Q cos [t/(LC)0.5] Q Q/(LC) 0.5 zero QQ²/(LC) 0.5 imax 1/(LC) 0.5
An inductor and a resistor are connected in series. When connected to a 60-Hz, 90-V (rms) source, the voltage drop across the resistor is found to be 55 V (rms) and the power delivered to the circuit is 18 W. (a) Find the value of the resistance. 22 (b) Find the value of the inductance. H
A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time after t = 0 that the current is a maximum is ?
In a home stereo system, low sound frequencies are handled by large "woofer" speakers, and high frequencies by smaller "tweeter" speakers. For the best sound reproduction, low-frequency currents from the amplifier should not reach the tweeter. One way to do this is to place a capacitor in series with the 9.0 Ω resistance of the tweeter; one then has an RLC circuit with no inductor L (that is, an RLC circuit with L = 0). What value of C should be chosen so that the current through the tweeter at 200 Hz is half its value at very high frequencies?