Current, Resistance, and Electromotive Force

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1 Week 5 Current, Resistance, and Electromotive Force )الشرح واألفكار الرئيسية( النوتات األساسية تتكون النوت من عشرة أسابيع. يحتوي كل نوت على شرح وحلول ألمثلة وتمارين من هوموركات وامتحانات سابقة. نوتات األمثلة والتمارين اإلضافية يتوفر على الموقع نوتات األسابيع لألمثلة والتمارين اإلضافية من واقع هوموركات وامتحانات سابقة. حقوق النوت لتعميم الفائدة فإني أتيح حقوق النسخ وإعادة اإلصدار وشروحات الفيديو لكل البشر سواء لبعض األجزاء أو الكل. واتساب ) ( يتم تنقحة النوت وتحديثها وإضافة الجديد إليها بشكل دوري. نتشوق النتقادك الهادف. الماضي ال يساوي المستقبل. لطلب نسخة ملونة مجانا )1(

2 Current, Resistance & Electromotive Force مصطلحات وقوانين الشابتر: Charge: q (C) Current: I (A) I = q t Voltage: V (V) (also called potential) Current Density: J (A/m 2 ) V = I R n: Free electrons per cubic meter (electrons/m 3 ) (شحنة االلكترون الواحد) q: C ρ: Material Resistivity (Ω. m) J = I/A J = n q v d v d : Dift speed (m/s) R: Resistance (Ω) ρ = A R L (Ω. m) L: Resistance length (m) R = R ο [1 + α (T T ο )] E: Electric Field (N/C or V/m) E = J ρ (V/m) ε: Electromotive force (V) ε = V + I r (internal resistance) أغلب المشكالت هي مجرد فرص لكنها ترتدي الزي الرسمي. )2(

I = Q t = 420 (80) (60) = 0.0875 C/s Or A J = n q v d 0.0875 π (0.0013) 2 = (5.

3 I = Q t = 420 (80) (60) = C/s Or A J = n q v d π (0.0013) 2 = ( ) ( ) v d v d = m/s إذا كنت تجهل كل من عدوك ونفسك فتأكد أنك في خطر. )3(

Q = I t = (5.00) (1.00) = 5.00 C The number of electrons is Q e = 3.12 1019 c) J = = v d = = I (π 4) D 2 5.00 (π 4) (2.05 10 3 ) 2 = 1.51 106 A m 2 J n q (1.51 10 6 ) (8.5 10 28 ) (1.60 10 19 ) = 1.

4 Q = I t = (5.00) (1.00) = 5.00 C The number of electrons is Q e = c) J = = v d = = I (π 4) D (π 4) ( ) 2 = A m 2 J n q ( ) ( ) ( ) = m s = mm s d) If (I) is the same, (J = I /A) would decrease and (v d ) would decrease. The number of electrons passing through the light bulb in إذا أعطيت الفقير سمكة سددت جوعه ليوم أما إذا change. 1.00) (s would not علمته الصيد تكون قد سددت جوعه طوال العمر. )4(

I A = n q v d v d = 4.85 π (1.025 10 3 ) 2 (8.5 10 28 ) (1.

5 I A = n q v d v d = 4.85 π ( ) 2 ( ) ( ) = m/s L = v d t t = 6,574 s = 110 min I A = n q v d v d = m/s L = v d t t = 26,542 s = 442 min c) v d α 1 d 2 إذا أقبل الشتاء لم يعد الربيع بعيدا. )5(

I = 55 0.65 t 2 t Q = I dt 0 8.0 s = (55 0.65 t 2 ) dt 0 = [55 t 0.217 t 3 ] 0 8.0 = 329 C I = Q t = 329 8.

6 I = t 2 t Q = I dt s = ( t 2 ) dt 0 = [55 t t 3 ] = 329 C I = Q t = = 41.1 C s = 41.1 A إذا كنت ترغب باستكشاف بحار جديدة يجب عليك أوال أن تتحلى بالشجاعة الالزمة لمغادرة الشاطئ. )6(

7 R = V I = = Ω ρ = A R L = π ( ) 2 (0.811) 1.5 = Ω. m R = R ο [1 + α (T T ο )] 15 (17.2) = (0.811) [1 + α (92 20 )] α = (C ο ) 1 = (C ο ) 1 إن التفكير أصعب األعمال وهذا هو السبب في أن قليلين من يختارونه كعمل. )7(

c) E = ρ J = ρ 20 [1 + (T T 0 )] ( I π r 2) = (5.25 10 8 ) [1 + (0.0045) (120 20 12.5 )] ( π (0.0005) 2) = 1.21 V m R = ρ L A = ρ L π r 2 = (7.61 10 8 ) (0.150) π (0.

8 c) E = ρ J = ρ 20 [1 + (T T 0 )] ( I π r 2) = ( ) [1 + (0.0045) ( )] ( π (0.0005) 2) = 1.21 V m R = ρ L A = ρ L π r 2 = ( ) (0.150) π (0.0005) 2 V = E L Or = (1.21) (0.150) = V V = I R = (12.5) (0.0145) = V = Ω )8( إن المشكلة التي ال نعرفها ال يمكن تصحيحها كما المرض الذي ال يمكن تشخيصه ال يمكن عالجه.

9 R = ρ L A A = ρ L R Volume = A L = ρ L2 R = ( ) (3.50) = m 3 m = (density) V = ( ) ( ) = 15 g إذا رأيت نيوب الليث بارزة فال تظن أن الليث يبتسم. )9(

10 E = J ρ = I A ρ I = E A ρ = (0.49) (π ( ) 2 ) ( ) = 11.1 A V = E L = (0.49) (6.4) = V c) V = I R R = V I = إذا طلب الصديق شيئا فال = Ω 11.1 مجال لقول أنظرني غدا. )11(

11 = (C 0 ) 1 (Table 25.2) Let T 0 = 0 C and T = 11.5 C R = R 0 [1 + (T T 0 )] R 0 = = R 1 + (T T 0 ) (0.0004) ( ) = Ω = (C 0 ) 1 (Table 25.2) Let T 0 = 0 C and T = 25.8 C R = R 0 [1 + (T T 0 )] = (0.0160) [1 + ( ) ( )] = Ω Nichrome, like most metallic conductors, has a positive (α) and its resistance increases with temperature. For carbon, (α) is negative and its resistance decreases as (T) increases. إذا فكرت أكثر فغالبا ستختصر مسافات كبيرة. )11(

E = 24.0 V I = 4.00 A V ab = E I r r = E V ab I (24.0) (21.2) = 4.00 = 0.700 Ω V ab I R = 0 R = V ab I = 21.2 4.00 = 5.

12 E = 24.0 V I = 4.00 A V ab = E I r r = E V ab I (24.0) (21.2) = 4.00 = Ω V ab I R = 0 R = V ab I = = 5.30 Ω The voltage drop across the internal resistance of the battery causes the terminal voltage of the battery to be less than its (emf). The total resistance in the circuit is (R + r = 6.00 Ω) I = = 4.00 A إذا فكرررت فرري أهررداف صررغيرة فتوقررع إنجررازات ضئيلة فكر في أهداف كبيرة وستفوز بنجاح هائل. )12(

E = J ρ = I A ρ = 125 π (0.05) 2 (1.72 10 8 ) = 2.74 10 4 V/m V = E L = (2.74 10 4 ) (100,000) = 27.

13 E = J ρ = I A ρ = 125 π (0.05) 2 ( ) = V/m V = E L = ( ) (100,000) = 27.4 V E = P t = V I t = (27.4) (125) (60 60) = J = 12.3 MJ أجه ل الناس م ن ترك يقين ما عنده لظن ما عند الناس. )13(

14 Open switch: V ab = ε = 3.08 V Closed switch: 3.08 = V + I r = r r = Ω V = I R R = V I = 1.8 Ω )14( أخطر األضرار التي يمكن أن تصيب اإلنسان هو ظنه السيئ بنفسه.

15 There is a single current path so the current is the same at all points in the circuit. Assume the current is counterclockwise and apply Kirchhoff s loop rule I ( ) 8.0 = 0 I = ( ) 17.0 = A Our calculated (I) is positive so (I) is counterclockwise, as we assumed. V b I (1.6) = V a V ab = 16.0 (0.471) (1.6) = 15.2 V Note: If we traveled around the circuit in the direction opposite to the current, the final answers would be the same. )15( ما تخاف منه سيقع إذا داومت على تفكيرك فيه.

P = V2 R 100 = (120)2 R R = 144 Ω c) P = V2 R 60 = (120)2 R R = 240 Ω I 100 W = P V = 100

16 P = V2 R 100 = (120)2 R R = 144 Ω c) P = V2 R 60 = (120)2 R R = 240 Ω I 100 W = P V = = A I 60 W = 60 أعط اهتمام أكثر لما تقوم به = 0.5 A 120 وسيخرج على نحو أفضل. )16(

17 Europe: P = V2 R 100 = (220)2 R R = 484 Ω United States: P = V2 R = (120)2 484 = 29.8 W I = P V = 29.8 إذا كنت ذا رأي فكن = A 120 فيه مقداما فإن فساد الرأي أن تترددا. )17(

18 By definition p = )18( P, use P = V I, V = E L and I = J A L A (E) is related to (V) and (J) is related to (I), so use (P = V I) p = V I L A V L = E and I A = J So p = E J (J) is related to (I) and (ρ) is related to (R), so use (p = I 2 R) p = I2 R L A I = J A and R = ρ L A So p = J2 A 2 ρ L L A 2 = ρ J 2 c) (E) is related to (V) and (ρ) is related to (R), so use (p = V 2 R) V2 p = R L A V = E L and R = ρ L A So p = E2 L 2 L A ( A ρ L ) = E2 ρ For a given material (ρ constant), p is proportional to J 2 or to E 2 أغلب من يعملون أفضل ال يعملون ساعات أطول.

P = V I = (12) (60) = 720 W U = P t = (720) (1 60 60 ) = (720) (3,600 ) = 2.

0565 900 = (6.3 10 5 ) ( 1,000 L ) = 0.063 L 1 c) Energy = (power) (time) U = P t t = U P = (2.6 106 ) 450 = 5,800 s = 97 min = 1.

19 P = V I = (12) (60) = 720 W U = P t = (720) ( ) = (720) (3,600 ) = J For gasoline the heat of combustion is L c = J kg ρ = m V m = ( ) ( ) = kg V = m ρ = = ( ) ( 1,000 L ) = L 1 c) Energy = (power) (time) U = P t t = U P = ( ) 450 = 5,800 s = 97 min = 1.6 h The battery discharges at a rate of (720 W for 60 A) and is charged at a rate of (450 W), so it takes longer to charge than to discharge. إذا لم تتمتع بما لديك فلن تتمتع بما عند غيرك. )19(

V = I R 3.5 Ω 12 V I = V R P useful = I 2 R = 12 25 = 0.48 A = (0.48) 2 (25) = 5.76 W 25 Ω P loss = I 2 r = (0.

20 V = I R 3.5 Ω 12 V I = V R P useful = I 2 R = = 0.48 A = (0.48) 2 (25) = 5.76 W 25 Ω P loss = I 2 r = (0.48) 2 (3.5) = W loss% = ( ) = 12.3% )21( بداخل كل صعوبة تواجهها تكمن فرصة أو فائدة متساوية أو أكبر.

E I r I R = 0 I = E r + R = 12.0 1.0 + 5.0 = 2.00 A P = E I = (12.0) (2.00) = 24.0 W P = I 2 r = (2.00) 2 (1.0) = 4.0 W c) P = I 2 R = (2.00) 2 (5.0) = 20.

21 E I r I R = 0 I = E r + R = = 2.00 A P = E I = (12.0) (2.00) = 24.0 W P = I 2 r = (2.00) 2 (1.0) = 4.0 W c) P = I 2 R = (2.00) 2 (5.0) = 20.0 W Note: The rate of production of electrical energy in the circuit is (24.0 W). The total rate of consumption of electrical energy in the circuit is (4.00 W W = 24.0 W). So both are equal. إذا لم تقفز فلن تعرف أبدا معنى الطيران. )21(

P = V2 R R = V2 P = (120)2 540 = 26.7 Ω P = V I I = P V = 540 120 = 4.5 A c) Assuming that (R = 26.

22 P = V2 R R = V2 P = (120)2 540 = 26.7 Ω P = V I I = P V = = 4.5 A c) Assuming that (R = 26.7 Ω) d) P new = V2 R = (110) = 453 W P = V2 R P α 1 R (larger) بداية النجاح أن ينبع من إمكاناتك أنت دون التطلع إلمكانات وممتلكات اآلخرين. )22(

ρ = A R L = ((π/4) (0.0025)2 ) (0.104) 14.0 = 36.5 10 9 Ω. m V = E L = I R c) I = E L R = (1.28) (14) 0.104 = 172.3 A J = n q v d J = E ρ = 1.28 (3.

23 ρ = A R L = ((π/4) (0.0025)2 ) (0.104) 14.0 = Ω. m V = E L = I R c) I = E L R = (1.28) (14) = A J = n q v d J = E ρ = 1.28 ( ) = A m 2 v d = = J n q ( ) ( ) ( ) = 2.58 mm/s تذكر أن الشمس حين تغرب تأخذ جزء منك كل يوم إلى غير رجعة. )23(

24 I 1 = I 2 = 2.5 ma I = 2.5 ma Copper c) d) E = J ρ = ρ I A E 1 = ( ) (π 4) ( ) 2 ( ) = V/m ( ) E 2 = (π 4) ( ) 2 ( ) = V/m V = E L = E 1 (1.2) + E 2 (1.8) أحب دائما أن يقول لي الناس انك ال تستطيع أن تفعل ذلك = 0.18 mv ألنهم كلما يقولون لي ذلك أعمله بجدارة. )24( L1 = 1.2 m L 2 = 1.8 m V =?

25 I = E R + r 96.0 = ( ) = A P = I 2 R = (3.288) 2 (28.0) = W The total heat needed is: Cup: Q = m c T = (0.130) (910) ( ) = 1, J Water: Q = m c T = (0.200) (4,190) ( ) = 11,145.4 J Total: Q = 12, J t = Q P = 12, = s إذا كان هم الربان المحافظة على سالمه السفينة فسفينته لن تبرح الميناء. )25(

4 V V ab = E + I r E + (3.5) r = 9.4 Solving, E = 8.4 + (1.5) r 8.

26 The battery with the (1.5 A) current is sketched in figure shown: V ab = 8.4 V V ab = E I r E (1.5) r = 8.4 The battery with the (3.5 A) current is sketched in figure shown: V ab = 9.4 V V ab = E + I r E + (3.5) r = 9.4 Solving, E = (1.5) r (1.5) r + (3.5) r = 9.4 r = = 0.20 Ω E = (1.5) (0.20) = 8.7 V إذا ما أتيت األمر من غير بابه ضللت وإن تقصد إلى الباب تهتد. )26(

R = ρ L A = (5.0) (1.6) π (0.050) 2 = 1.0 103 Ω = 1 kω V = I R = (100 10 3 ) (1.

27 R = ρ L A = (5.0) (1.6) π (0.050) 2 = Ω = 1 kω V = I R = ( ) ( ) = 100 V c) P = I 2 R = ( ) 2 ( ) = 10 W أساسيات السعادة في هذه الحياة ثالثة: شيء نفعله وشيء نحبه وشيء نأمل في حدوثه. )27(

E 1 E 2 I (r 1 + r 2 + R) = 0 I = (E 1 E 2 ) (r 1 + r 2 + R) = (12.0 8.0) (1.0 + 1.0 + 8.0) = 0.

28 E 1 E 2 I (r 1 + r 2 + R) = 0 I = (E 1 E 2 ) (r 1 + r 2 + R) = ( ) ( ) = 0.4 A P = I 2 R + I 2 r 1 + I 2 r 2 = I 2 (R + r 1 + r 2 ) = (0.4) 2 ( ) = 1.6 W إذا ما لم يكن لك حسن فهم أسأت إجابة وأسأت سمعا. )28(

29 Continued Solution: c) p 12.0 V = E 1 I = (12.0) (0.4) = 4.8 W d) p 8.0 V = E 2 I = (8.0) (0.4) = 3.2 W e) Total rate of production of electrical energy = 4.8 W. Total rate of consumption of electrical energy = = 4.8 W, which equals the rate of production, as it must. إما أن تتعب لتحصل على ما تحب أو ستجبر نفسك على حب ما تحصل عليه. )29(

30 No current flows through the capacitor when it is fully charged. With the capacitor fully charged. I = E R 1 + R 2 V C = Q C = ( ) ( ) = 4.00 V V R1 = V C = 4.00 V I = V R 1 R 1 = = A V R2 = I R 2 = (0.667) (4.00) = V E = V R1 + V R2 = = 6.67 V إن المستحيل كلمة غير فرنسية. )31(

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