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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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