Physics Tutor In Florida-AP Physics C: Electricity and Magnetism Answers-2021

2021

AP Physics C: Electricity and Magnetism Answers

-

& ue-I

V = IR Q = JV

Q:Do ete

Que-2

2=

>FafTeoer

use ②=

2o

RC

,

t0 SI Wt = NB

AW

PB.

PE w=

/ 24 -

ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS

Neutron mass, mn

27

kg

10

27

kg

9.11 10

31

1.67

Electron mass, me Avogadro’s number, N 0

1

8.31 J (mol K)

Boltzmann’s constant, k B

1.38

10

23

e

1.60

10

19

C

1 electron volt, 1 eV

1.60

10

19

J

Electron charge magnitude,

kg

10 23 mol

6.02

R

Universal gas constant,

10

1.67

Proton mass, m p

Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface,

c

3.00

10 m s

G

6.67

10

11

1u

1.66

10

27

kg

931 MeV c 2

Planck’s constant,

h

6.63

10

34

Js

4.14

10

25

8.85 10

12

e0

Vacuum permittivity, Coulomb’s law constant, k Vacuum permeability, 1 atmosphere pressure,

PREFIXES Factor Prefix Symbol

mole, hertz, newton, pascal, joule,

1 4 pe0 m0

Magnetic constant, k

m kg s A K

kg 2

9.8 m s2

g

1 unified atomic mass unit,

meter, kilogram, second, ampere, kelvin,

N m2

J K

hc

UNIT SYMBOLS

8

m0 4 p

1 atm mol Hz N Pa J

1.99

Jm C

2

1.24 Nm

109 N m 2

9.0

7

(T m) A

1 10

7

(T m) A

1.0

105 N m 2

watt, coulomb, volt, ohm, henry,

W C V W H

15

eV s

3

10 eV nm

2

C2

10

4p

10

1.0

105 Pa

farad, tesla, degree Celsius, electron volt,

F T C eV

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q 0 30 37 45 53 60 90

109

giga

G

sin q

0

12

35

2 2

45

3 2

1

106

mega

M

cos q

1

3 2

45

2 2

35

12

0

103

kilo

k

tan q

0

3 3

34

1

43

3

10 2

centi

c

10 3

milli

m

6

micro

m

10 9

nano

n

12

pico

p

10

10

The following assumptions are used in this exam.

I. The frame of reference of any problem is inertial unless otherwise stated.

II. The direction of current is the direction in which positive charges would drift.

III. The electric potential is zero at an infinite distance from an isolated point charge.

IV. All batteries and meters are ideal unless otherwise stated.

V. Edge effects for the electric field of a parallel plate capacitor are negligible unless otherwise stated.

ADVANCED PLACEMENT PHYSICS C EQUATIONS MECHANICS

Ãx

x

ax t

Ãx 0

x0

1 2 at 2 x

Ãx 0 t

Ãx2

Ãx 0 2

2ax x

a

F m

Fnet m

F

dp dt

J

p

F dt

m FN

DE

W

K

1 2 mà 2

P

dE dt

P

F v

DUg

Ã2 r

r

F t net I

I 2

I

r dm

mr

kDx

Us

1 k Dx 2

x

xmax cos( wt

T

2p w

p

Iw

2p

Tp

2p

1 2 Iw 2

w

w0

at

q

q0

w0 t

FG UG

1 2 at 2

2

1 f

Ts

rw r

acceleration energy force frequency height rotational inertia impulse kinetic energy spring constant length angular momentum mass power momentum radius or distance period time potential energy velocity or speed work done on a system position coefficient of friction angle torque angular speed angular acceleration phase angle

Fs

2

mi xi mi

x cm

K

w2r

t

a

L

F dr

mg Dh

ac

Ã

Dp

mv

Ff

t

x0

a = E= F = f = h = I = J = K = k = = L = m= P = p = r = T = t = U= v = W= x = m = q = t = w = a = f =

ELECTRICITY AND MAGNETISM

m k

FE q

E

DV

DV

Q C

UC

r2

Gm1m2 r

i

i

= = = = = = = = = = = =

N =

qi ri

= = = = = = = V= v = r = F = k = P Q q R r t U

1 q1q2 4pe0 r

k e0 A d

1 Cs

Ci

1 C i i

area magnetic field capacitance distance electric field emf force current current density inductance length number of loops of wire per unit length number of charge carriers per unit volume power charge point charge resistance radius or distance time potential or stored energy electric potential velocity or speed resistivity flux dielectric constant

FM

qv

B d

dQ dt

1 QDV 2

1 C DV 2

2

B m0 I

dB

m0 I d r 4p r 2

R

r A

F

I d

E

rJ

Bs

m0 nI

I

Nevd A

FB

I

DV R

e

E d

e

L

UL

1 2 LI 2

g

Gm1m2

1 4pe0

qV

Cp

n

E dr

UE

C

F I J L

dV dx

Ex

V

e

Q e0

E dA

I f

A B C d E

1 q1q2 4pe0 r 2

FE

Rs 1 Rp

P

Ri

i

i

I DV

1 Ri

B

B dA

dI dt

d FB dt

ADVANCED PLACEMENT PHYSICS C EQUATIONS GEOMETRY AND TRIGONOMETRY Rectangle A bh Triangle

A

1 bh 2

Circle

A

pr2

C

2p r

s rq Rectangular Solid V wh Cylinder 2

V

pr 

S

2p r 

CALCULUS

A = area C = circumference V = volume S = surface area b = base h = height  = length w = width r = radius s = arc length q = angle

df dx

d f du du dx

d n x dx

nx n

d ax e dx

aeax 1 x

d ln ax dx d sin ax dx

a cos ax

d cos ax dx

s

x n dx

r

q 2p r 2

eax dx

Sphere

dx

a sin ax 1

n

ln x

V

x

S

4p r 2

cos ax dx sin ax dx

Right Triangle

b2

c2

sin q

a c

cos q

b c

tan q

a b

a

c q

a 90°

b

xn 1, n

1

1 ax e a

4 3 pr 3

a2

1

a 1 sin ax a 1 cos ax a

VECTOR PRODUCTS   A B AB cos q   A B AB sin q

1

Begin your response to QUESTION 1 on this page. PHYSICS C: ELECTRICITY AND MAGNETISM SECTION II Time—45 minutes 3 Questions Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in this booklet in the spaces provided after each part.

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1. The circuit shown above is composed of an ideal 10 V battery, three resistors and three capacitors with the values shown, and an open switch S. The capacitors are initially uncharged. Switch S is now closed. (a) Calculate the current through R1 ⑭U immediately after switch S is closed. when switch is closed, all capacity F:

f

well act as

a

short circuit

01 A

Switch S has been closed for a long time, and the circuit has reached a steady state. (b) Calculate the potential difference across R1.

M. URn

=(t30x60 (

x 100

100) =stox

=

8.3vou

(c) 30 +60 i. Calculate the charge stored on the positive plate of capacitor C2. ⑭m Now potential difference across capaciter 48C.=10-8.3=1.7 volt 102MC RK=JXIT= ii. Is the charge stored on capacitor C3 greater than, less than, or equal to the charge stored on capacitor C2 ? a

(i)(17)=

=

At

A

_____ W Greater than _____ Less than _____ Equal to Justify your answer.

Chavez incapacitor

(3,

0

=

3 x 17=20x180x17=34MC

Continue your response to QUESTION 1 on this page.

Switch S is then opened. (d) i. Determine the current through R1 ↑ immediately after the switch is opened.

Facross

Rn)

=

8

ii. Calculate the current through R2 A immediately after the switch is opened.

URz=170

Volt

then

1R

=Lee110

=.0566 Amp

(e) On the axes below, sketch a graph of the potential difference V across capacitor C2 M as a function of time t if switch S is opened at time t = 0. Label the maximum value.

06TV=

Capacitor C3 ⑬ is replaced by t wo 10 μF capacitors connected in series, switch S is closed, and the circuit reaches equilibrium. Switch S is then opened at time t = 0. (f) For t > 0, would the sketch of a graph of the new voltage across C2 as a function of time be above, below, or My the same as the sketch for part (e) ? _____ Above _____ Below _____ The same Justify your answer.

-

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then

Replaced

d two

by

louf capacity series

then

↳ will be

instead

stence

5l

of

f

200

f

total capacity

decreases 2 RO

decrease. new curve

In

the m will also

will be below the previous curve.

Begin your response to QUESTION 2 on this page.

2. Students perform an experiment to study the force bet ween t wo charged objects using the apparatus shown above, which contains t wo identical conducting spheres. The upper sphere is attached to an insulating string, which can be used to move the sphere downward. The lower sphere sits on an insulating rod, which is on an electronic balance. The electronic balance is zeroed before the lower sphere and insulating rod are in place.

For the first trial, a charge of Q is placed on each sphere and then the upper sphere is slowly moved downward. The students measure the distance d bet ween the centers of the spheres and the magnitude F of the force that appears on the electronic balance. The recorded data are shown on the graph of F as a function of o 12 shown below. d i. Draw a line that represents the best fit to the points shown.

ii. Use the graph to calculate the charge Q.

F

=

8

aTito

=

@

(to)

0"

as) wit.

#

(Yar)

=

10500

↓

-

slope

of

the

graph

#10500x158N 0

2000

-

1500 x

=

106

ex109x e

↓

172-90)

32xex109"72x188C

t

02.5

(T2)

iii. On the graph on the previous page, draw a circle around the data point that was taken when the distance bet ween the centers of the spheres was the least.

previous

on

↳shown

page)

iv. Determine the distance bet ween the centers of the spheres for the data point indicated above.

=02-5

hTd=

O11M

v. What physical quantity does the vertical intercept represent?

Justify your answer.

The Vertical intercept

the

force

infinitely

acting of

on

when

the

away, the

so the

scale

the lower sphere

represents top sphere is

is

and

only

the

face

weight

insulatingrad.

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The experiment is extended by collecting additional data points, which appear on the right side of the graph shown above. The new data points do not follow the linear pattern seen with the first points. The group of students tries to explain this discrepancy. (b) One student suspects that charge is slowly leaking off the top sphere. Could this explain the discrepancy? ~ Yes _____ No ____ Justify your answer.

Later the force measured is lesser

than in

actual

charge

value

only

then

explain

decrease the

theory.

Continue your response to QUESTION 2 on this page. i. On the circles representing the spheres below, use a single “+” sign on each sphere to represent the locations of highest concentration of the excess positive charges. t

t

ii. Explain how this rearrangement could be responsible for the discrepancy. on

a

move thus

conductor

excess

due

any

where

the

repelling

to

charge is

free

requestion

force

decreases.

to

(d) A third student suggests that the experiment be modified so that the top sphere is given a negative charge that is equal in magnitude to the positive charge given to the bottom sphere. i. On the circles representing the spheres below, use a single “+” sign on the bottom sphere to represent the location of highest concentration of the excess positive charges. Use a single “−” sign on the top sphere to represent the location of the highest concentration of the excess negative charges.

-

->

ii. For a separation distance equal to that of the data point indicated in part (a) (iii), would the magnitude of the force reading with spheres of opposite charges be greater than, less than, or equal to the magnitude of the force reading with spheres of the same charges? _____ Greater than _____ Less than _____ Equal to Justify your answer.

t

-

opposite charge.(Attraction well decrease on

lower

will

be

same

in

Normal

sphere, less than

charge.

force

take

exerted

thus the when the

reading

by of

place) the

scale

the

scale

sphere had the

Begin your response to QUESTION 3 on this page.

3. A thin, conducting ring of area A and resistance R is aligned in a uniform magnetic field directed to the right and perpendicular to the plane of the ring, as shown. At time t = 0, the magnitude of the magnetic field is ↑Bo B0.

At t = 1 s, the magnitude of the magnetic field begins to decrease according *S to the equation , B where b has units of T◊s.

(t)=

(a) Derive an equation for the magnitude of the induced current I in the ring as a function of t for t > 1 s. Express your answer in terms of b, A, R, t, and physical constants, as appropriate.

& (PA). =181=1E (B.x) A -

=AP F

=

DV

(= t2) =

EP

=

AP

↳ R = 2.0 Ω, and ⑬ Assume A = 0.50 m2, b = 0.50 TSG ◊s. (b) Calculate the electrical energy dissipated in the ring from t = 1 s to t = 2 s. #=

=

(0d+=) #Rdt=()redt

TBR.dt=bf

EFIELTLEEmBEBTfTsIsoxe -

Le+

.0091

=>

F

Continue your response to QUESTION 3 on this page.

The ring is then rotated so that the plane of the ring is aligned at a 30° angle to the magnetic field, as shown.

The magnitude of the magnetic field is reset to a magnitude of B0 at a new time t = 0 and again begins to o decrease at t = 1 s according to the equation , where b has units of T◊s.

(c) Will the amount of energy dissipated in the ring from t = 1 s to t = 2 s be greater than, less than, or equal to the energy dissipated in part (b) ? _____ Greater than _____ v Less than _____ Equal to Justify your answer.

As

the

pass ais

rotates, fewer magnetic

ring through less

the

then

ring, P=

E

is

less

is less.

field

than

lines

before,

will

dd

isles

I

I

The ring is now mounted on an axle that is perpendicular to the magnetic field. The magnitude of the magnetic field is now held at a constant B0 ⑭ = 0.50 T, as shown. The ring rotates about the axle, and the emf e induced in the ring as a function of time t is shown on the graph.

T2 sep (from (d) Calculate the angular speed w of the rotating ring in rad/s. the W= IB Physics Tutor in, Alachua Florida, IB Physics Tutor in, Altamonte Springs Florida, IB Physics Tutor in, Anna Maria Florida, IB Physics Tutor in, Apalachicola Florida, IB Physics Tutor in, Apopka Florida, IB Physics Tutor in, Atlantic Beach Florida, IB Physics Tutor in, Auburndale Florida, IB Physics Tutor in, Aventura Florida, IB Physics Tutor in, Avon Park Florida, IB Physics Tutor in, Bal Harbour Florida, IB Physics Tutor in, Bartow Florida, IB Physics Tutor in, Bay Harbor Islands Florida, IB Physics Tutor in, Boca Raton Florida, IB Physics Tutor in, Bonita Springs Florida, IB Physics Tutor in, Boynton Beach Florida, IB Physics Tutor in, Bradenton Florida, IB Physics Tutor in, Brooksville Florida, IB Physics Tutor in, Cape Canaveral Florida, IB Physics Tutor in, Cape Coral Florida, IB Physics Tutor in, Casselberry Florida, IB Physics Tutor in, Celebration Florida, IB Physics Tutor in, Chipley 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z=zD=Hrad/sec -314

grain

radian/sec

e-ddThomaxdEA--BAcor

(e) Calculate the magnitude of the maximum emf eMAX induced in the ring.

--BA & -

-

compare to

=

coswe)

BA(W SInwt) buth

emac

e

z=

=

=

BAW SIncot

to Sin Not

B A w

(0.50) (0.50)

=

=0.79 volt

3.14 Ve)

The ring now begins to rotate at an angular speed 2w. (f) On the graph below, draw a curve to indicate the new induced emf e in the ring. The dashed curve shows the emf induced under the original conditions.

W=

2T

T

-

original

condition

New condition

aw=I* **) T

=

-

New

to

=2HBAW

time

perced =IseC

N

G

New time period will be

half

the

original

time period

But,

20:

NBAW

becomes

Justify your sketch, specifically identifying and addressing any similarities or differences bet ween the sketch and the original graph.

INB AW double

AP® Physics C: Electricity and Magnetism 2021 Free-Response Questions

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