Mt 1 Solutions

7/29/2019 Mt 1 Solutions

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Problem 1(3 pts)

Lightbulbsland2areglowingwithaboutequalbrightness. lfthefrequencyoftheACsourceisraised

significantly, what happens to light bulb 1 and light bulb 2?

Circle the correct answer.

Both bulbs become brighter

The brightness of each bulb remains constant

Bulb 1 becomes brighterthan bulb 2

Bulb 2 becomes brighter than bulb 1

Both bulbs become dimmer

Problem 2 (8 points)

N-F,{ar \rn3

i,4froc{*^rs

W'fflr\" d}

dn^S * $",c-'

-br ca^ng-- *f t'1.€ f

14.Si$"t *^^ ctu

Consider the circuit above.

(4 pts) I throw the switch to position a and t+tu

battery? I e I

lg= |

-L*-R \

(a pts) tthen throfi-theTiTdrlo position b

the time constant of that exponential decay

it for this circuit.)

Wl*#*r's-?ffi

a and wait a longtime. What

11l.onr- ii{lc- ''aj'

ition b and observe that the ct

decay? (You don't have to de

IIL

-.t-€LK I qR-

flowing from the

att.4- R- f'n

,* a$k,u zu f **6 *tr

exponentially. What is

consta nt, just evaluate

fPo tjs '"tll

?Lz

tt-,;o R'-s * fi'

3'/.'{"45 :" eR

e current

*tyC.tO C 'l

nt dec-ays

the time




( ,r'-1,i,'t :it, '... rtr' ,it.,ir:l',,'i,'.r.

\' i:,'. ;tl{ L-tttir'iLt / tlr ll,,'.1::r'r itr,it'it

.t'"-'-{.

/

\r'/hat is the magnitude and direction of the magnetic field at point P? Show your work.

raiiluS a,/_/'

Y

i




{3 ill'.I hook up a neon sign transformerto a load with resistance R1ou6

The transformer primary is rated 120 V and the secondary is rated 12,000 v.

From the standpoint of the wall plug, the circuit looks like a 120 Vo. into a simple load resistor on the

primarysideasshownbelow. WhatistheequivalentL20VcircuitresistanceR"ointermsof Rro"a?

rlLJ

t.T.rrrr,S |rt-t D tS

.-? S rs

rl Ru*& = T-; R"f

k?=.+ 2-

J-<_y--t-

fi

h,-"rf - R*L

hls*-:

Nr

V5*aVg

uNp

M-?

R, = il*Y



l* -*-;l*xxI

lxxx


I

I

lx

l"lxIl"

I

c.

d.

e.

| - -lr-llx x xI

l*xxX

X

xX

Tl --B",ra-l Y*7

F,V

x x x x x x "i

lx x x x x x x x x x .1J

The loop above is pulled at a constant velocity v to the right as shown. A uniform magnetic field points

into the page. ln terms of x, l, v, B, and R

a. (5 pts) What is the currept in the loop?.

b 2pts*;*s:.lH

,._4,t"u*

(2 pts) Mark the direction of the net electromagnetic force on the figure above' i *&

(5 pts) What is the rate of work done by the hand?

t#+

!'.)e [- , ] JJc :d+-

f. (5 pts) What is the thermal

fD = -i 'J n#-,

f .cb- E\

power generation ilj!" t..tit

T-"'*** \ u"g* '/*.@'1

! rr'r

\Y"i -___--

tor R?

XXXXXXXX

xxxxxxx

xxxxxxx

XXXXXXX

xxxxxxx




A triaxi.rl catrle is mircle of .rrr inulPr conciuctor

rrf rirclius rt, srlrrounclercl bv tn'o tlrirr cr.lirrclriic.rl shells; one rvitlr r.tc{itrs lr .rrrcl thesecottcl rvitlr rilc'litls (', <ls ai't,rtr'r', ltelorr,. A urrifc,rnr a.,ront clensitv /,, t'l.rvs to tlreright throtrglr the itrtrer cortcltrctor. Tl're current rettrrns r.i.t the trr,., -*hetts; e.rch slrellc.rrries ltrrt/? current tr.rck to tlre left, w,here lt.,t is tlre total current c.rrrieri trr. tlreirrrrer cclncltrctclr

a. (2 pts) Give an expression that relates l1o, and Jo . =furob' (5 pts) Give expressions for the magnetic fierd from 0 < r < infinity rr4J.

$v,Jfr-- AG-etu B zrf f _o lAaLua

3

wA1TU

ffi,A.

(Problem continued on next page)

b

&r D Ar t& B= )b5;*Q:lftx'

fAr \-z'c B=in.ts-a,'b, and c on the

maximum magnetic field value on the y -axis.

Ft' b. r /^L

B* qg3*. 4*.eSTf

qrr



e.

(2 pts)The self inductance per unit length is L. lf I remove the cylindrical shell at radius b, and

instead let allthe current return on the shellat radius c, how would the self-inductance of the

cable change? Would it@,decrease, or stay the same? (circle the answer)

For the following questions, assume all the current is returned at radius c as described above.

(5 pts) What is the inductance of a 1 meter length of the cable due to the flux between a and c?

L-

I matcr

6 f B,IA-}=/gE

dh* lu"a.t+.t J

B**z1rr

L -( * I

N,L

"-+t = r pLo - ZL+O

AAr -z:tT( -

and c?na. (5 pts) What is the magnetic energy density for all points betwe

HJft\

(5 pts) lntegrate the magnetic energy density to find the energy stored between a and c for 1

meter of cable.

u=

tts eff

J'l"c..ni

.[r ),1 JL

? Lrs"

Problem 6, continued

F*r 41z.f L 1-

%ln7

-e-"6 -L

-€rr\ r2-

-Lg nL

ILoTz Z11 I

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Mt 1 Solutions