!"#$%&'()*+),(-.&(/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+(