R P#E(faculty.polytechnic.org/physics/3 A.P. PHYSICS 2009... · ^+8(R 1=8 ! V 1=4 V R 3=1 ! R 5=1 !...
3
!"#$%&' )*+), -.& /0"/102 03 "14 5#" ,)6 3&/#473+ ,+8 R 1 = 8 ! V 1 = 4 V R 3 = 1 ! 9+8 :.92;3 2.& /1""&42 04 &9/. "&3032#"< R 5 = 1 ! R 2 = 5 ! V 2 = 12 V R 4 = 3 ! =&%#> 03 94 &4%9"?&7 /0"/102 >02. /1""&423 7&@4&7 #4 9 $&32A?1&33 $9303 B'#"& 9$#12 /1""&42 7&@40C#43 92 2.& &47 #5 2.& D"#$%&'8E R 1 = 8 ! V 1 = 4 V R 3 = 1 ! R 5 = 1 ! R 2 = 5 ! V 2 = 12 V R 4 = 3 ! i 1 i 2 i 1 + i 2 )+8 9+8 :.92;3 2.& /1""&42 04 &9/. "&3032#"< R 1 = 8 ! V 1 = 4 V R 3 = 1 ! R 5 = 1 ! R 2 = 5 ! V 2 = 12 V R 4 = 3 ! i 1 i 2 i 1 + i 2 L 1 L 2 V 1 ! i 2 R 3 ! i 2 R 2 ! i 1 + i 2 ( ) R 1 = 0 4 ! i 2 1 () ! i 2 5 () ! i 1 8 () ! i 2 8 () = 0 " 8i 1 + i 2 14 ( ) = 4 " i 1 = !14i 2 + 4 8 " i 1 = !1.75i 2 + .5 -.& !"#$ $&'()"! >93 13&7 2# 7&@4& 2.& /1""&42 2."#1?. 2.& * #.' "&3032#"F 3# >02. #4%G 2># 14H4#>43F >& 4&&7 2# 13& *""+ $&'()"!, 2# @403. 2.& 293H+ I;J& 07&4C@&7 2.& %##D3 947 70"&/C#4 #5 2"943J&"3& #4 2.& 3H&2/.+ L 1 : V 1 ! i 2 R 3 ! i 2 R 2 + i 1 R 4 + i 1 R 5 ! V 2 = 0 4 ! i 2 1 () ! i 2 5 () + i 1 3 () + i 1 1 () ! 12 = 0 " ! i 2 6 () + i 1 4 ( ) = 8 " 4i 1 ! 6i 2 = 8 " 4 !1.75i 2 + .5 ( ) ! 6i 2 = 8 " ! 7i 2 + 2 ! 6i 2 = 8 " i 2 = !.46 L 2 : BK#2& 2.92 2.&"& 9"& 3&J&"9% >9G3 2# 3#%J& 2.&3&+ I;J& 13&7 94 9%?&$"90/ 9DD"#9/. 0432&97 #5 9 '92"0LA7"0J&4 /9%/1%92#" 9DD"#9/.+ M02.&" >0%% 7#N8 O+8 P#E R 1 = 8 ! V 1 = 4 V R 3 = 1 ! R 5 = 1 ! R 2 = 5 ! V 2 = 12 V R 4 = 3 ! i 1 i 2 i 1 + i 2 L 1 L 2 i 1 = !1.75i 2 + .5 = !1.75 !.46 ( ) + .5 = 1.3 A i 3 = i 1 + i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i 2 P V 1 = W battery1 !t " W battery1 = P!t = #1.84 joules sec ( ) 120 sec ( ) = #222 joules $+8 -.& &4&"?G 7&%0J&"&7 $G &9/. $9R&"G '9H&3 13& #5 2.& D#>&" "&%9C#43.0D+ Y#" E U+8 V 1 P V 1 = i 2 V 1 = !.46 A ( ) 4 V ( ) = !1.84 W R 1 = 8 ! V 1 = 4 V R 3 = 1 ! R 5 = 1 ! R 2 = 5 ! V 2 = 12 V R 4 = 3 ! (!.46A) L 1 L 2 (.84A) (1.3A) :.G 2.& 4&?9CJ& 30?4< -.& ,) J#%2 $9R&"G 03 5#"/04? /1""&42 -!." 2.& U J#%2 $9R&"G+ -.03 03 #DD#302& >.92 $9R&"G 1319%%G 7# B2.&G 9"& 7&30?4&7 2# D12 &4&"?G 042# 2.& 3G32&'8+ Q3 31/.F 2.& $9R&"G 04 2.03 /93& /94 $& 2.#1?.2 #5 93 7&D%&C4? &4&"?GF 31??&323 9 4&?9CJ& D#>&" "9C4?+ Z4#>04? 2.& D#>&"F >& /94 >"02&E i 1 i 2 i 3
Transcript of R P#E(faculty.polytechnic.org/physics/3 A.P. PHYSICS 2009... · ^+8(R 1=8 ! V 1=4 V R 3=1 ! R 5=1 !...
!"#$%&'()*+),(-.&(/0"/102(03("14(5#"(,)6(3&/#473+(((
,+8(
R1 = 8 !
V1 = 4 V
R3 = 1 !9+8(:.92;3(2.&(/1""&42(04(&9/.("&3032#"<(
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
=&%#>(03(94(&4%9"?&7(/0"/102(>02.(/1""&423(7&@4&7(#4(9($&32A?1&33($9303(B'#"&(9$#12(/1""&42(7&@40C#43(92(2.&(&47(#5(2.&(D"#$%&'8E(
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
i1i2
i1 + i2
)+8(
9+8(:.92;3(2.&(/1""&42(04(&9/.("&3032#"<(
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
i1i2
i1 + i2
L1
L2
V1 ! i2R3 ! i2R2 ! i1 + i2( )R1 = 04 ! i2 1( ) ! i2 5( ) ! i1 8( ) ! i2 8( ) = 0 " 8i1 + i2 14( ) = 4
" i1 =!14i2 + 4
8 " i1 = !1.75i2 + .5
-.&(!"#$%$&'()"!%>93(13&7(2#(7&@4&(2.&(/1""&42(2."#1?.(2.&(*(#.'("&3032#"F(3#(>02.(#4%G(2>#(14H4#>43F(>&(4&&7(2#(13&(*""+%$&'()"!,(2#(@403.(2.&(293H+((I;J&(07&4C@&7(2.&(%##D3(947(70"&/C#4(#5(2"943J&"3&(#4(2.&(3H&2/.+(
L1 : V1 ! i2R3 ! i2R2 + i1R4 + i1R5 ! V2 = 04 ! i2 1( ) ! i2 5( ) + i1 3( ) + i1 1( ) ! 12 = 0 " ! i2 6( ) + i1 4( ) = 8 " 4i1 ! 6i2 = 8 " 4 !1.75i2 + .5( ) ! 6i2 = 8 " ! 7i2 + 2 ! 6i2 = 8 " i2 = !.46
L2 :
BK#2&(2.92(2.&"&(9"&(3&J&"9%(>9G3(2#(3#%J&(2.&3&+((I;J&(13&7(94(9%?&$"90/(9DD"#9/.(0432&97(#5(9('92"0LA7"0J&4(/9%/1%92#"(9DD"#9/.+((M02.&"(>0%%(7#N8(
O+8(
P#E(
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
i1i2
i1 + i2
L1
L2
i1 = !1.75i2 + .5 = !1.75 !.46( ) + .5 = 1.3 A
i3 = i1 + i2
= 1.3 + !.46( ) = .84 A
947(2.&(/1""&42(2."#1?.(2.&(*(#.'("&3032#"(03E(
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
i2
PV1=
Wbattery1
!t " Wbattery1 = P!t
= #1.84 joulessec( ) 120 sec( )
= #222 joules
$+8(-.&(&4&"?G(7&%0J&"&7($G(&9/.($9R&"G('9H&3(13&(#5(2.&(D#>&"("&%9C#43.0D+((Y#"((((((E(((
U+8(
V1PV1
= i2V1
= !.46 A( ) 4 V( ) = !1.84 W
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
(!.46A)
L1
L2
(.84A)
(1.3A)
:.G(2.&(4&?9CJ&(30?4<((-.&(,)(J#%2($9R&"G(03(5#"/04?(/1""&42(-!."(2.&(U(J#%2($9R&"G+((-.03(03(#DD#302&(>.92($9R&"G(1319%%G(7#(B2.&G(9"&(7&30?4&7(2#(D12(&4&"?G(042#(2.&(3G32&'8+((Q3(31/.F(2.&($9R&"G(04(2.03(/93&(/94($&(2.#1?.2(#5(93(7&D%&C4?(&4&"?GF(31??&323(9(4&?9CJ&(D#>&"("9C4?+((((Z4#>04?(2.&(D#>&"F(>&(/94(>"02&E(
i1i2
i3
$+8(-.&(&4&"?G(7&%0J&"&7($G(&9/.($9R&"G('9H&3(13&(#5(2.&(D#>&"("&%9C#43.0D+((Y#"((((((E(((
[+8(
V2
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
L1
L2PV2= i1V2
= 1.3 A( ) 12 V( )
= 15.6 Watts =Wbattery2
!t " Wbattery2 = PV2
!t
= 15.6 joulessec( ) 120 sec( )
= 1872 joules
(!.46A)
(.84A)
(1.3A)i1
i2
i3
\+8(
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
L1
L2
/+8(-.&(&4&"?G(7&%0J&"&7(2#(2.&("&3032#"3(03(2.&(39'&(93(2.&(&4&"?G(70330D92&7($G(2.&'F(3#(1304?(2.&(D#>&"("&%9C#43.0D(5#"("&3032#"3F(>&(/94(>"02&E(
PR1= i3
2R1
= .84 A( )2 8 !( ) = 5.65 joules
sec
As PR1=
Wresistor1
"t # Wresistor1 = PR1
"t
= 5.6 joulessec( ) 120 sec( )
= 672 joules
(!.46A)
(.84A)
(1.3A)i1
i2
i3
K#2&(2.92(2.&(9/219%(3#%1C#4('9419%(%0323(2.03(93(\*](X#1%&3($&/913&(2.&G(13&7(+*U\(9'D3(93(2.&0"(/1""&42+(
]+8(
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
L1
L2
Y#"((((((E(
PR2= i2
2R2
= !.46 A( )2 5 "( ) = 1.06 joules
sec
As PR2=
Wresistor2
#t $ Wresistor2 = PR2
#t
= 1.06 joulessec( ) 120 sec( )
= 127 joules
(!.46A)
(.84A)
(1.3A)i1
i2
i3
K#2&(2.92(2.&(9/219%(3#%1C#4('9419%(%0323(2.03(93(,)*(X#1%&3(93(2.&G(13&(A+U\)(9'D3+(
R2
/+8(B/#42;78(
*+8(
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
L1
L2
Y#"((((((E(
PR3= i2
2R3
= !.46 A( )2 1 "( ) = .21 joules
sec
As PR3=
Wresistor 3
#t $ Wresistor 3 = PR3
#t
= .21 joulessec( ) 120 sec( )
= 25.2 joules
(!.46A)
(.84A)
(1.3A)i1
i2
i3
K#2&(2.92(2.&(9/219%(3#%1C#4('9419%(%0323(2.03(93()[+\(X#1%&3+(
R3
/+8(B/#42;78(
^+8(
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
L1
L2
Y#"((((((E(
PR4= i1
2R4
= 1.3 A( )2 3 !( ) = 5.07 joules
sec
As PR4=
Wresistor 4
"t # Wresistor 4 = PR4
"t
= 5.07 joulessec( ) 120 sec( )
= 609 joules
(!.46A)
(.84A)
(1.3A)i1
i2
i3
K#2&(2.92(2.&(9/219%(3#%1C#4('9419%(%0323(2.03(93(\,\(X#1%&3(93(2.&G(13&(,+O,(9'D3+(
R4
/+8(B/#42;78(
,6+8(
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
L1
L2
Y#"((((((E(
PR5= i1
2R5
= 1.3 A( )2 !( ) = 1.69 joules
sec
As PR5=
Wresistor5
"t # Wresistor5 = PR5
"t
= 1.69 joulessec( ) 120 sec( )
= 203 joules
(!.46A)
(.84A)
(1.3A)i1
i2
i3
K#2&(2.92(2.&(9/219%(3#%1C#4('9419%(%0323(2.03(93()6[(X#1%&3+(
R5
/+8(B/#42;78(
,,+8(
R1 = 8 !
V1 = 4 V
R3 = 1 !
R5 = 1 !R2 = 5 !
V2 = 12 V
R4 = 3 !
L1
L2
_304?(2.&(>#"H`&4&"?G(J9%1&3(D"#J07&7($G(2.&($##H(B5#"(9//1"9/G(39H&8F(2.&(31'(#5(9%%(2.&(&4&"?G(70330D92&7($G(2.&("&3032#"3(03E((
(!.46A)
(.84A)
(1.3A)i1
i2
i3
7+8(
Wdonebyresistors = 687 + 128 + 25.6 + + 616 + 205 = 1661.6 joules
-.&(/.&'0/9%(&4&"?G(/#4J&"30#4(04($9R&"G(((((((D"#J07&7(,**6(X#1%&3(B9//#"704?(2#(2.&($##H8+((P#(>.92(
V1
.9DD&4&7(2#(2.&(9DD"#L0'92&%G())6(X#1%&3(#5(V%&aA#J&"W(&4&"?G(D"#J07&7($G(2.92($9R&"G<((I2(>&42(042#(/.9"?04?(1D($9R&"G(((((((2#(2.&(214&(#5(A)))(X#1%&3(B2.03(03(2.&(9DD"#L0'92&(#J&"%9Gb2.&(703D9"02G(03(71&(2#("#147A#T(&""#"8+((
V2
&+8(-.&(2#29%(&4&"?G(70330D92&7($G(2.&("&3032#"3(03F(93(3292&7(9$#J&F(,\\,+\(X#1%&3(B9DD"#L0'92&%G8+((-.03('92/.&3(B9?904F(93(>93(3292&7(9$#J&8(2.&(9'#142(#5(&4&"?G(B4&28(D12(042#(2.&(3G32&'($G(2.&($9R&"0&3+(
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