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PRS: LC Circuit<br />

Consider the LC circuit at<br />

right. At the time shown the<br />

current has its ~<br />

value. At this time<br />

-<br />

D<br />

L<br />

c- l<br />

0% ~ The charge 00 the capacitor has its maximum value""" 11\ It). }LJt<br />

'" ~ The magnetic field is zero<br />

0% The eleclrlc field has its maximum value .-!!JIt{1<br />

. . J<br />

-<br />

f<br />

0% 4. The charge on the capaCitor IS zero<br />

0% . Don't have a clue<br />

~I~" (e~r''w)<br />

td<br />

'3 rv \'Vt'lo ~U '( <<br />

PRS: LC Circuit<br />

In the LC circuit at right the e<br />

current is in the direction<br />

==<br />

shown and the charges on<br />

the capacitor have the signs F<br />

shown. At this time,<br />

-Q +Q<br />

:r<br />

0% @ I is increasing and Q is increasing<br />

0% I is increasing and Q is decreasing<br />

0% 3. I is decreasing and Q is increasing<br />

'"<br />

'"<br />

4. I is decreasing and Q is decreasing<br />

5. Don't have a clue<br />

11'<br />

J\'C~'el/<br />

()J<br />

,,~<br />

PRS Answer: LC Circuit<br />

D<br />

Answer: 4. The current is<br />

maximum when the charge<br />

on the capacitor is zero<br />

Current and charge are exactly 90 degrees out of<br />

phase in an ideal LC circuit (no resistance). so when<br />

the current is maximum the charge must be<br />

identically zero.<br />

t1,now<br />

(htij f; € tl<br />

f ~C'.)\ vd lJ~<br />

PRS Answer: LC Circuit<br />

Answer: 2. I is increasing;<br />

Q is decreasing<br />

With current in the direction<br />

shown, the capacitor is<br />

discharging (Q is decreasing).<br />

But since Q on the right plate is positive, I must be<br />

increasing. The positive charge wants to flow, and<br />

the current will increase until the charge on the<br />

capacitor changes sign. That is, we are in the first<br />

quarter period of the discharge of the capacitor,<br />

when Q is decreasing and positive and I is<br />

increasing and positive.<br />

t"·»<br />

.)'1'<br />

~-f ,.<br />

4."t\\ '(I!J<br />

(}\f\'1 ",,.>/<br />

PRS: LC Circuit<br />

The plot shows the charge ' ..... =-.---,="<br />

on a c~ r (black curve) ~ .<br />

and the current through it<br />

(red curve) after you turn<br />

off the power supply. If yOU ! 4J<br />

J~ I<br />

r .... lfOS)<br />

" 0<br />

C~v'(tE<br />

Core. l' L<br />

~O wht-ti<br />

PRS Answer: LC Circuit<br />

Answer:<br />

1. T Lag will increase 11 ..... '<br />

, I ·<br />

s~~· t++++-I~+-I+J'<br />

!-<br />

. ,,,,.~<br />

---.:.--::.:--;i,;,'0>'<br />

,-....<br />

Putting in a core increases the inductor's<br />

inductance and hence decreases the natural<br />

frequency of the circuit. Lower frequency means<br />

longer period. The phase will remain at 90' (a<br />

quarter period) so T lag will increase.<br />

---.oc.<br />

\vtl l Tl-~<br />

1,[ l; vU{<br />

}W4>" 7' L<br />

h,,~~erSr Mv' Jcz ) { el\o(l,V\ lp/ th 'q<br />

J

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