1. Xtra Edge February 2012 - Career Point

30.
φ
E
Or
Let a source of alternating e.m.f. be connected to a
circuit containing a pure inductance only, Fig.
Suppose the alternating e.m.f. supplied is
represented by
E = E0
sin ωt
L
If dI/dt is the rate of change of current through L at
any instant, then induced e.m.f. in the inductor at the
same instant is = – L dI/dt . The negative sign
indicated that induced e.m.f. opposes the change of
current. To maintain the flow of current, the applied
voltage must be equal and opposite to the induced
voltage
⎛ dI ⎞
i.e. E = – ⎜ – L ⎟ = Eo sin ωt
⎝ dt ⎠
E0 or dI = sin ω t dt
L
Integrating both sides, we get
E0 I =
L
E0 =
L
∫sin ωt dt
A
⎛ cosωt
⎞ E0 ⎜ – ⎟ = – cos ωt
⎝ ω ⎠ ωL E0 = –
ωL sin ⎟ ⎛ π ⎞
⎜ – ωt
⎝ 2 ⎠
E0 or I = sin (ωt – π/2)
ωL …(i)
The current will be maximum i.e. I = I0, when sin
(ωt– π/2) = maximum = 1.
E0 From (i), I0 = × 1
ω L
Putting in (i), we get
I = I0
sin( ωt
– π/
2)
…(ii)
This is the form of alternating current developed.
t
CHEMISTRY
XtraEdge for IIT-JEE 78 FEBRUARY 2012
1
Ammonical AgNO3
CH3CH2CH2CHO ⎯ ⎯⎯⎯⎯⎯⎯→CH3CH2CH2COOH Butanal
( Tollens'
reagent)
Butanoic
acid
2. 3-Amino-2-chloro butanamide
3. These are partly produced in body.
Ex. Histidine and arginine
4. yes, because O2 is paramagnetic
5. In B.C.C no. of effective atoms are = 2
In F.C.C no. of effective atoms are = 4
6. In lyophillic colloids affinity is present between
dispersed phase and dispersion medium and
therefore it is more stable.
7. r = k [NO] 2 [H2]
8. 6-Amino 3-chloro 4-hydroxy hexanamide
9. (i) Aldol condensation : Two molecules of an
aldehyde or a ketone having at least one α-hydrogen
atom, condense in the presence of a dilute alkali to
give β-hydroxy aldehyde or β-hydroxy ketone.
O
OH
CH3–C + HCH2CHO
Dil. NaOH CH3–C–CH2CHO
H
H
Ethanal Ethanal Aldol
(ii) Gabriel phthalimide synthesis : Phthalimide on
treatment with ethanoic KOH gives potassium
phthalimide which on heating with a suitable alkyl halide
gives N-substituted phthalimides. These upon hydrolysis
with dil HCl under pressure give primary amines.
CO
CO
Phthalimide
NH + KOH (alc)
–H2O
C2H5I, ∆
–KI
CO
N–C2H5
CO
N-Ethylphthalimide
CO
N
CO
– H +
Pot. Phthalimide
H + / –H2O
COOH
C2H5NH2 +
COOH
Ethylamide
Phthalic acid