2018-10-01_Physics_For_You

M =

φ

i

Ÿ M

a

R

=

μ 0 2

272 / =

μ 0 2

2 2

a

p/R

? p = 7

7. (a) : C^1

L

L

Þ

C 2 C+^12 C

We know that q = qm cos Zt

i = qmZ cos ωt+π





2 

, i = i 0 cosωt+π

2

Maximum current i 0 = qmZ

where ω=

()+

















1

LC 12 C

Maximum charge on (C 1 + C 2 )

qm =

i

(^0) iL 01 CC 2
ω

=+()

Maximum charge on C 1

=

+

×+()

C

CC

(^1) iLCC
12
012 = iC

L

(^01) CC 12 +

8. (b) : In LC oscillation energy is transferred C to L
   or L to C.

Maximum energy in L =

1

2

LImax^2

Maximum energy in C =

q

C

max

2

2

Equal energy will be when

1

2

LI^2 =

1

2

1

2

LI^2

max









I =

1

2

Imax Ÿ I = Imax sinZt =

1

2

Imax

Zt =

π

4

or

2 π

T

t =

π

4

or t =

T

8

t =

1

8

2 π LC =

π

4

LC

9. (c) : UU

U

max

==^1 , max

220

LI^2

⇒=









1

2

1

2

1

2

2

0

LI LI^2

⇒−Ie− =

t I

0

220

2

1

2

[]/τ

⇒=−=

− −

et/τ 1

1

2

21

2

⇒−=

 −







t

τ

ln

21

(^2)
⇒=
−









t τln^2

21

⇒=

−









t L

R

ln^2

21

10. (c) : For (LR) circuit

cos q =^3

5

Ÿ q = 53° Ÿ XL =

4

3

R 1

For (CR) circuit, cosθθ=⇒=⇒=

1

2

60 XRC (^32)
In LCR, power factor is 1 i.e., (XC – XL) is zero.
? (^) XXLC=⇒^4 RR=
3

123 Ÿ^

R

R

2

1

4

33

=

11. (c) : e equation of a semi-circular wave is
    x^2 + y^2 = a^2 or y^2 = a^2 – x^2

I

a

aydx

a

rms= −

+

∫

1

2

2

I

a

axdx

a

221 a 2

rms 2

=−

−

+

∫ ()

=−− =−

+

−

+

∫

1

2

1

23

22 2

3

a

axdx

a

ax

x

a

a

a

a

()

=−+−











=

1

233

2

3

3

3

3

32

a

a

a

a

aa

I

a

rms==a

2

3

2

3

2

12. (b) : As resistance of the lamp

R

V

P

==s =

2

0

1002

50

200 Ω

e rms value of current is

I

V

R

== =

100

200

1

2

A.

So when the lamp is put in series with a capacitance

and run at 200 V ac, from V = IZ, we have

Z

V

I

== =

200

12

400

(/)

Ω

Now as in case of CR circuit,ZR

C

=+^2  

1 2

ω

i.e., R

C

2

1 2

+  = 160000

ω

or,

1

16 10 200 12 10

2

42 4

ωC







 =×−=() ×

(^1) 12 10 2
ωC

=×

C=

××

1

100 π 12 10^2

F==^100

12

50

π 3

μ

π

FFμ

13. (d) : e

d

dt

Na

dB

dt

=− ==

φ 2

5 volt

14. (d) : Aer a long time, steady state is reached in
    which impedance due to inductor (ZL for dc) is