ADINA INSTITUTE OF SCIENCE AND TECHNOLOGY

SAGAR

SUBMITTED TO SUBMITTED BY-

SHIVANGI MISHRA

MECHANICAL ENGG.

Q.1Find the maxima and minima of the function

Solution:-

For maixima or minima of f ,we have ⋯⋯⋯⋯(1) ⋯⋯⋯⋯(2)Subtracting (2) from (1), we have

3(-)+12(y-x) = 0

3(x-y)(x+y)+12(y-x) 0

3(x-y)(x+y-4) 0

x=y or x+y=4

Putting x=y in eq. (1) we get,

3+12-6 = 0

+-21 = 0

=-7 or 3

Thus f may have maxima or minima at ( -7,-7) & (3,3)

Pitting in eq.(2) we get

3-63+12(4-=0

3-12-15 = 0

-4-5 = 0

()() = 0

= 5 , -1

= -1 , 5

Thus f may have maxima or minima (-1,5) and (5,-1)

Hence f has a maxima at (-7,-7) and minima (3,3)

Maximum Value

=+-63(-7-7)+12(-7)(-7)

=784

Minimum Value

=+-63(3+3)+12×3×3

=27+27-63(6)+12×9

=-216

Ans..

Q.2

Prove that current in purely resistive circuit is in phase with applied AC voltage at in purely capacitive circuit leads applied voltage by 90° draw their wave forms.

ANS.

AC CIRCUIT CONTAINING RESISTANCE ONLY;-

The circuit containing a pure resistance of R ohms is Ohms is shown in fig.

Let the alternataing Voltage applied across the circuit be given by the equation-

u=sinωt ……………….(1)

Then the instantaneous value of current flowing through the resistance will be

==sinω ……………….(2)

The value of current will be maximum when

ωt = 90°

sinωt =1

=

 

Susitituting these value in eq. (2) we get.

=sinωt …………………..(3)

PHASE ANGLE:-

Hence in on AC circuit on AC circuit containing pure resistance , current is in phase with the Voltage.

POWER:-

Instantaneous power

P=VI

AC CIRCUIT CONTAINING PURE CAPACITOR ONLY:-

The circuit containing a pure capacitor c is shown in fig.

Let the alterbnating Voltage applied across the circuit be given by

V=sinωt ………………………(1)

Change on the capacitor at any instant

q=cv

Current flowing through the circuit

Vmsin ωt

csin ωt

=ccosωt

sin(ωt+

=sin(ωt+

Where xc= the opposition offered to the flow of alternating current by a pure capacitor is called capacitive reactance.

The value of current will be maximum when

sin(ωt+1

Substituting these value in eq.(2) we get

sin(ωt+ ……………..(3)

PHASE ANGLE:-

Hense is AC circuit containing pure capacitance current leads the voltage 90° .

POWER:-

Instantaneous power

P=vi

P=0

POWER CURVE:-

 Q.3

Pseudo Unimolecular ReactionThe reactions having molecularity  out order of reaction is one are

called pseudo unimolecular reactions.

Thus order of reaction is one but molecularity of the reaction is two.

Thus order of reaction is one but molecularity of reaction is two.

Thus order of reaction is one but molecularity of reaction is three.

Similarly the reactions having molecularity 

but order of reaction is two are called pseudo bimolecular reactions.

Q.4

Differences between AC &DC CircuitDC: Direct CurrentA DC current is a current that does not change direction in time.

DC circuits works on DC power supply,

For DC circuit only resistance are connected . the inductance

And capacitance are relevantin ac circuit.

Example of DC circuits:

Portable flashlight circuit.

Internal circuit inside a DMM to measure resistance.

Circuit to control a dimmer light using a potentiometer, as you will on Thursday.

AC CIRCUIT:-AC: Alternating CurrentAn AC current is a current that changes direction in time.

It works on ac power supply.

Applications:-

Power generation power plants.

Design of radios and radio stations.

THANKS FOR YOUR ATTENTION…