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Chapter 31: Q74P (page 940)

An oscillating LC circuit has an inductance of 3.00mHand a capacitance of 10.0渭F. Calculate the (a) angular frequency and (b) period of the oscillation. (c) At time t =0, the capacitor is charged to200渭Fand the current is zero. Roughly sketch the charge on the capacitor as a function of time.

Short Answer

Expert verified

a). Angular frequency is5.77脳103rad/sec.

b). Period oscillation is 1.09脳10-3sec

c). The graph is plotted for a charge on the capacitor as a function of time.

Step by step solution

01

Given

  1. Inductance is 3.00mH.
  2. Capacitance is 10.0渭贵.
  3. Charge is 200渭C.
02

Determining the concept

Use the formula for angular frequency for LC circuit in terms of inductance and capacitor. Then use the formula for angular frequency and find the time.

The formula is as follows:

03

(a) Determining the angular frequency

Angular frequency:

In an oscillating LC circuit, angular frequency is given as follows:

蝇=1LC

蝇=13脳10-3脳10脳10-6

蝇=5.77脳103rad/sec

Hence, angular frequency is 5.77脳103rad/sec..

04

(b) Determining the period oscillation

Period oscillation:

The time period is as follows:

蝇=2蟺T5.77脳103=2蟺TT=1.09脳10-3sec

Hence, period oscillation is 1.09脳10-3sec.

05

(c) Determining the sketch charge on the capacitor as a function of time

Sketch charge on the capacitor as a function of time

The charge on the capacitor is given as follows:

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Most popular questions from this chapter

Figure 31-25 shows the currentand driving emf 蔚for a series RLC circuit. (a) Does the current lead or lag the emf? (b) Is the circuit鈥檚 load mainly capacitive or mainly inductive? (c) Is the angular frequency 蝇dof the emf greater than or less than the natural angular frequency 蝇?

In an oscillating LCcircuit, when 75% of the total energy is stored in the inductor鈥檚 magnetic field,(a) What multiple of the maximum charge is on the capacitor? (b) What multiple of the maximum current is in the inductor?

In a series oscillating RLC circuit,R=16.0惟,C=31.2渭F,L=9.20mH, and sinvdtwith 蔚m=45.0Vand 蝇d=3000rad/s. For timet=0.442msfind (a) the ratePgat which energy is being supplied by the generator, (b) the ratePCat which the energy in the capacitor is changing, (c) the ratePLat which the energy in the inductor is changing, and (d) the ratePRat which energy is being dissipated in the resistor. (e) Is the sum ofPC,PL ,PRand Pggreater than, less than, or equal to ?

In an oscillating LCcircuit withC=64.0渭F, the current is given byi=(1.60)sin(2500t+0.680), where tis in seconds, Iin amperes, and the phase constant in radians.(a) How soon aftert=0will the current reach its maximum value? (b) What is the inductance L? (c) What is the total energy?

Figure 31-19 shows three oscillating LC circuits with identical inductors and capacitors. At a particular time, the charges on the capacitor plates (and thus the electric fields between the plates) are all at their maximum values. Rank the circuits according to the time taken to fully discharge the capacitors during the oscillations greatest first.
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