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Integral Calculus

Blazing goIITian

Joined:	12 Dec 2007
Post:	1249

27 Jun 2009 15:40:40 IST

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QUESTION OF THE WEEK - 2

None

Well last time I gave a simple qs in physics as the qs of the week based on Leak current but this time I have increased the level of the competition. This qs is specially for class 12 and pass out student and is not from the syllabus of JEE so those who follow strict JEE pattern can leave it.

Question : You all know about circuits of physics and the toughest one are the LCR circuit right. So lets take an LCR circuit not the AC one but DC one. Taking AC will make the qs even out of my mind so let me stick to the AC one. See the diagram

now in the figure the resistor has rsistance R and the inductor has self induction L and the EMF of cell is E and the capacitor is C .

Now the qs is

1 : Find the differential equation for finding charge as a function of time

2 : convert differential eqn of the form

d²y/dx² + A dy/dx + B y + C =0

3 : convert the equation to the form

d²y/dx² + Pdy/dx + Qy = 0

4 : Now the master qs solve the above eqn by substituting y= e ^UX F(x)

where u is to be determined so as to make the eqn as

d²y/dx² = Kx

Find the U as a function of P and find K . Hence solve the equation

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Comments (7)

bladeX -rise of a new sun

Blazing goIITian

Joined: 12 Dec 2007

Posts: 1249

27 Jun 2009 15:41:13 IST

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WAIT FOR A MINUTE WHILE THE QS IS BEING LOADED

bladeX -rise of a new sun

Blazing goIITian

Joined: 12 Dec 2007

Posts: 1249

27 Jun 2009 15:56:52 IST

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DATE : 27th june ,2009END DATE : 4th july , 2009

Decoder

Blazing goIITian

Joined: 1 Apr 2007

Posts: 1084

27 Jun 2009 18:04:53 IST

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well...bladex ..u r doing nice job....out here...!!!u hold this...i hold the algebra section... Question is still oen goiitians make it !!!

bladeX -rise of a new sun

Blazing goIITian

Joined: 12 Dec 2007

Posts: 1249

27 Jun 2009 20:20:58 IST

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OK FRIENDS LET ME GIVE YOU ONE HINT :

THE EQN IS THOUGH OF SECOND ORDER BUT IF YOU FOLLOW MY STEPS OF SUBSTITUTION YOU CAN SOLVE IT.

SAVVEJ

Blazing goIITian

Joined: 4 May 2007

Posts: 697

7 Jul 2009 10:13:38 IST

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1. E - Ld²q/dt² - q/C - Rdq/dt =0 ---------->differential eqn for charge as fnc of time.

2. d²q/dt² + {R/L}dq/dt +q/LC -E/L=0 ----------> differential equation for charge in the required form.

3.i dont know how to eliminate that constant without changing the variable q.plzz help on this part.

bladeX -rise of a new sun

Blazing goIITian

Joined: 12 Dec 2007

Posts: 1249

7 Jul 2009 11:01:53 IST

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so ok change the variable. Take : q/LC - E/L = t

SAVVEJ

Blazing goIITian

Joined: 4 May 2007

Posts: 697

7 Jul 2009 12:29:33 IST

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3.putting q/LC -E/L =z

we get

d²z/dt² +R/L dz/dt +z/LC=0 ---------->converted to the required form

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