Chuyên đề ôn thi đại học môn vật lý bài toán hộp đen

SỞ GD&ĐT VĨNH PHÚC
TR ƯỜNG THPT XUÂN HÒA
CHUYÊN ĐỀ ÔN THI ĐH MÔN VẬT LÍ
BÀI TOÁN HỘP ĐEN
Tác giả: Lê Anh Tuấn
GV môn Vật lí

PHẦN I: ĐẶT VẤN ĐỀ
"Bµi to¸n hép ®en"
 !!"#$%&'$(!)*$+,-#.
/+,##$0%1"& 2
Có nhiều phương pháp để xác định xem trong hộp đen có những phần tử
nào và xác định giá trị của chúng. 3!&!4,567
++,!&48&'96,:'
5giản đồ véc tơ*!/;%8&<!=
Đối tượng áp dụng là học sinh lớp 12A2 và12A3 trường THPT Xuân
Hòa.
PHẦN II: NỘI DUNG
a. C¬ së lý thuyÕt
>?4@+A9B&(C!/;$D
&EB6!CFGC'1C+,
E16C+H2IH ,JB'+,6
K%L&'AGCME2
DẠNG 1: N'AEO'A%P8%6D!+
C'2
Q#ϕ,'1C+,M'







π
≤ϕ≤
π
−
22
O
ϕR
ϕRS
ϕR
.T.
.U5.&,
V
.
WV
U
.TX
.X5U5.
V
U
RV
.
.TU
.U5.
V
U
WV
.
Y22Z Y22OZ YG22Z YG22OZ
(c.1.1) (c.1.2)

[ϕ[S
S[ϕ < π/2
NX
+,.
.4X5U5
.2V
.
WV
U
N
U+,X
.4X5U5
.2V
U
WV
.
Y22Z Y22OZ YA22Z YA22OZ
ϕ
\
U
\
U.
\
.
\
X5.
\
X
\
U5X

DẠNG 2: 2NO'A%&]'T<K'
ϕ^1C&+,C&O
S≤ϕ ’≤π.
L
>%&'&
!&'
J
>%&U!ω
YE_Z`ϕ = 0
N8a"
N<a
>%&.
+,bF
N<X
Y_2Z Y2Z Y2Z
ϕ^RS
ϕ^R
ϕ^Rπ
c'(+
 K
c'X
c'O.
c'U
c'OX
c'U
c'O.
Y2OZ
YG2O2OZ
YG2O2Z
Y2OZ

DẠNG 3:NO'A&]'T<O%LKX5U5.1
!8+H2
Q#ϕ^,'BC1O'$+HC
1O'OYS≤ϕ^≤π).
dc'X5Ue
• c'X5.
f
0 < ϕ^[
c'U5%
c'OXEU5%
c'U
c'OU52%
c'U2%
c'O.
Y2O2OZ
YA2OZ
Y2O2Z
[ϕ^[π
0 < ϕ^[
c'O.5
X^
c' O X^5
.
V
.
WV
U
0 < ϕ^[
c'  O X^5
.

V
U^
WV
.
c'OX^5
U^
c'OX^5
.
ϕ^RS
c'OX^5U^
ϕ^R
c'OX^5.
(a.3)
(b.3)
ϕ^RS
c'OX^5.^
ϕ^R
c'OX^5U
(e.3)
(f.3)
< ϕ^[
c'O.5X^ c'OU^5.
V
.
WV
U^
0 < ϕ^[
c'OU^5.
V
U^

WV
.
c'OX^5U^
c'OX^5.
(c.3.3)(c.3.1) (d.3.1) (d.3.2)(c.3.2)
*c'U5.eV
U
WV
.
YgCV
U
[V
.
9DZ
2. Ph¬ng ph¸p gi¶i chung:
hiHe
>=&'e
Q1C+,M',ϕ
Q16C+H,ϕ^
gCG,'6C5`=&ϕ5ϕ^5?G*<
6CE?G*<'e
j
c'O.5
X^
c' O X^5
.
V
.
WV
U

c'  O X^5
.
V
U^
WV
.
c'OX^5
U^
c'OX^5
.
< ϕ^[
c'OX^5U
c'OU5.^
V
.k
[V
U
0 < ϕ^[
c'OX^5.^
c'OX^5U
c'OU5.^
V
.k
WV
U
(i.3.1) (i.3.2) (i.3.3) (k.3.1) (k.3.2)
ϕ^RS
c'OU^5.^
V
U^

WV
.k
ϕ^R
c'OUk5%+,.k
V
Uk
RV
.k
ϕ^Rπ
c'O.^5U^
V
.^
WV
U^
(l.3) (m.3) (n.3)
0 < ϕ^[
c'OX5U^
[ϕ^[π
c'OX5.^
(p.3)
(q.3)
h
rR
C
1
L
rR
ZZ
UU
UU

tg
CL
rR
CL
+
ϖ
−ϖ
=
+
−
=
+
−
=ϕ
E$ϕ =R/Z.
h-;,&$($e$ϕ^R
O O O
O OL L
O OL
\ \ \
O\ \
+ −
2He
231213
uuu

+=
hiHOe
>?4@+A9e
l6;G,6'&'%GGCP%82

mCF6%MFP%&ộ$9@E(F+H6%M
F%G$9@*!/;&<1!=n+,C
,4G,6&&M2
B. CÁC VÍ DỤ MINH HỌA:
BÀI TẬP DẠNG 1:
B i à 1: .&=+o2l,&''A<K
XEUE.5GC 
pi
RSS
2
$
SSπYZqr
p
R
2
YpZ5RSSYsZ5.
R
π
3
10
3−
YtZ5%u9
pi
2>=&vl+,6%;BK2
Gi¶i:
mCF4C+'1+,+,&8a$%'
A4&YA22Z
'A,&'&'' %≠S2
>eRr
O

%→%R
( )
( )
Ω== 50
2
100
I
P
22
NE!6e%
O
hYV
U
V

Z
O
R
2
2
I
U
AB
⇒
( )
2
2
2
2
2

2
AB
CL
50
2
100
r
I
U
ZZ −=−=−
w
l
p
.
i
p
Q4%eV
U
RxSYΩ) ⇒UR
ππω
5
4
100
80
==
L
Z
YcZ
B i 2:à .&=+o2X
,GC%P5a.,

L
S
y
−
π
YtZl,&'&@&O%LKX
S
5U
S
5.&z(C2-E
+, p5i&'C6%;a\
 pi
!2mXRX

RySΩ=e

pN
RxS
O
$YSSπ
O
π
Z YZ

Ni
RwS
O
$YSSπZ YZ
l6;6KBl+,6%;B`2
Gi¶i:

l{pN5'1\
pN
+,e
ϕ
ΑΜ
R
4
1
1
π
ϕ
−=⇒−=
−
AM
C
R
Z
Y$H&9\
pN

f
π
>eV
pN

290
2
2
=+=
C

ZR
$%
A
Z
U
I
AM
AMO
2
0
==
→RO$YSSπ
f
π
ZYpZ
i M{Nie
230
I
U
Z
0
MB
MB
==
 YΩ). 3 +H      5  \
Ni
 $H&    9  
ϕ
ΜΒ
=

4
π
%l4<KX
S
+,U
S
Y0&YA22ZZ
>e
ϕ
Ni
R
1
4
tg
R
Z
0
L
0
=
π
=
⇒V
US
RX
S

>eV
Ni
RLS

2
R
2RRR
0
2
10
2
0
=+
3%eX
S
RLSΩ = V
US
+,U
S
R
π
=
ϖ
3,0
Z
0L
YcZ
|
l
p
X
i
N
.

BÀI TẬP DẠNG 2:
B i 1: à
.&'&(Cp^i^.^<!,'
'4&5a5%P2m$(BG}SSSc
V
M
F6Ca\
p^i^
ROYZ5\
i^.^
R
3
YZ5\
p^.^
RYZ+,M
'arRS
L
YpZ2
Q1(;\
p^.^
"$(8J6SSSc
V
Mv%
&7p^i^.^4&2-&p^i^.^<1=n>$n-&
p^i^<=ni^.^<=n$n>7%PB'4&C2
Gi¶i:
>=&'
ϕ
k1
pkik

+,
ik.k
=&p^i^.^&z(C8e

p^.^
R
p^i^
h
i^.^
'''''' CBBACA
UUU

+=
>G*uG}4@+A92Y=+oG8Z
>e
O O O
p^.^ p^i^ i^. ^ p^i ^ i^ .^
\ \ \ O\ 2\ 2$= + − α
RfhLO2O
L
$α
→$αR
p ^ i ^5 i^.^
\ \
L j
^
O w w
π π
→α= →ϕ =
>vπ W

p^ i ^5 i ^ . ^
^
\ \
O
π
ϕ >

>%8&]&p^i^+,i^.^T&'!<0%8p^i^.^
@&&'a&z(C+H' %PAYA2OZ2
>?<e
rR
( )
p^.^ p^.^
O
O
p^.^
U .
\ \
V
X V V
=
+ −
.v\
p^.^
R$5X5U5.R$
m_"8H9_
S
RSSSc
~
&,U4&<0YV

U
V
.
Z
O
"→
•V
U
V
.
•"&,!_"=V
U
"V
.
4&2
x
ϕ^
i^.^
\

p^i^
\

p^.^
\

α
&(
U .
V V−

"!_W_
S
=_
S
4Oπ_
S
UW
S

O _ .π

V
SU
≥V
S.
[RW
O O O O O
SU S.^ SU S.^  ^
~ ~ X ~ ~ \ \≥ → + > → >
>AG,\
p^i^
R\

R
OW\
i^.^
R
L
YZ
%8p^i^4,' %P5%8i^.^,a2

m_R_
S
RSSSc
V
V
S.
R
L
i^.^
\
L2S
r
= Ω
V
p^i^
R
O O L
p^i^
S
\
X V O2S
r
+ = = Ω
V
p^.^
R
( )
O
O L
p^.^

SU S.
\
X V V S
r
+ − = = Ω
Q4%XRS
L
Ω
BÀI TẬP DẠNG 3
B i 1:à
.&=+ol+,€,'A5&]'T<O
%LKe%P5' 4&+,a&z(C2.6
+!C

5
O
+,&A!CF4+,&'2-%P6
+!C%vH5%P&A!C!6!*2m&z*&p+,N+,
DB@&'5&A!CTOp5

TwSYZ2m&zp+,i
+,@5$(jSc
V
=&A!CTp56+!CT
:6%;wSYZ\
pN
+,\
Ni

2

π
2c'l+,€1
!,n>=&6%;B`2
Gi¶i:
y
€l

O


p i
N
m&zOBl+,€+H@&'5%&rR
Op2.<0!<aYAY_2ZZ2%l<%+,'
4&U2Ie%R
Ω== 30
2
60
I
U
gC€•1X+,U=1
AM
U
+,
MB
U
T*,
&'#+=4$H&9$+H2€<%PX
+,a.YAYG2LZZ2
Q4@+A9%%MF,F%=G,=+o2

>AG,erRp23%
\
%
Rr2%R2LSRLSYZ
g+e\
%
R
2
1
\
pN
→αRLS
S

>\
U
R\
pN
2$αRwS2$LS
S
RLS
3
YZ
3%eV
U
R
330
1
330
I

U
L
==
YΩ)
⇒UR
π
=
ω 100
330
Z
L
YcZ
I\
pN
+,\
Ni
+5$%β = α = LS
S
8e
\
X
R\
pi
2$βRwS$LS
S
RLS
3
YZ
⇒XR
330

I
U
R
=
YΩ)
\
.
R\
pi
2$βRwS$LS
S
RLSYZ
V
.
R
30
1
30
I
U
C
==
YΩ) ⇒.R
π3000
1
YtZ
CÁC BÀI TẬP TƯƠNG TỰ
i,e
.&=+oe
RSS

2
$SSπYZ2
S
l
p
%5U
i
N
m
pg
\

U
\

β
.
\

Ni
\

X
\


α
%
\


i0J%P (+,!6m2
2mm%&r

ROp+,LS
S
$+H
C2c<0' %2
O2mm&P=r
O
Rpq
pN
$+H
Ni
yS
S
2
2>7$v8a%8l2
G2-&l<O%LKYX5U5.Z2c6;l+,=&
6%;B`2
i, Oe .&=+o2
l,'A<O%LK5'4&5a5%P!_RjSc~q
\
pN
R\
Ni
R|jYZq \
pi
RjSYZq rRS5jp2
m_RSSc~5$($vB&Ni,
2

1
2
c0l<1!=n>=&6%;B`
-3ec'l@&' %RjSYΩ),UR
π
1
YcZ+,.R
f
S
−
π
i, L e.&=+o2
UR
)H(
2
1
π
q.R
π
−
25
10
2
YtZ

pi
RSS
2
$SSπYZ2l,&''<O%LK' 
4&5a+,%P2

\
pN
RSS
2
YZq
pN
+,
Ni

4
3π
2c0l<1!
=n>=&'HB`n
Bµi 4
.&pi@&'!7lT
<&'KY' 4&
EaZ+,GC%PX=+o2

l
p
X
i
N
l
p
.
i
U
N
Y%RSZ

l
i
p
X
-E+,p5i&'C;6%;a
OSS+,$(jSc~2>6%;BGC%PX*$v8a
%&pi,D2m5M'J&6%;
aG}5ffpYG}
O
pZ2iCM'$H&9
C1&pi2c0'!7<K,5=&6
%;B`2
Bµi 5 : .&=+o2

pi
 RSS
2
2$  SSπ  YZ2
.

R
π
−
5
10
3
YtZ2c'l<O
%LKX

5U5.2m.


R.
O
v
pN

2
π
$+H
Ni
5&
9
pi
,
6
π
+,rRS5jp2
c'l<=n>=&6%;B`2
-3e.<XRjS
3
qUR
2
π
YcZ
Bµi 6 : 
>%&''!7<aa2g('+H
@=vC'9M'
J'&'ϕ YS[ϕ[
2
π

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Bài tập 16:
Cho mạch điện AB gồm 3 linh kiện X, Y, Z mắc nối tiếp với nhau. Mỗi hộp
chỉ chứa một trong ba linh kiện cho trước: điện trở thuần, tụ điện và cuộc cảm.
Đặt vào hai đầu A, D của đoạn mạch một hiệu điện thế xoay chiều u
AD
=32
2
sin(2.π.f.t) (V). Khi f=100Hz thì U
X
=U
Y
=20V, U
Z

=16V, U
YZ
=12V (hiệu điện thế
giữa hai đầu Y và Z) và công suất tiêu thụ P=6,4W. Khi thay đổi f thì số chỉ của
Ampe kế giảm.
Hỏi X, Y, Z chứa những linh kiện gì? Tìm giá trị của chúng? Coi Ampe kế có
R
A
=0.

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