صفحة 64 - كتاب الفيزياء - الصف 12 - الفصل 2 - المملكة العربية السعودية

الكتاب: كتاب الفيزياء - الصف 12 - الفصل 2 | المادة: الفيزياء | المرحلة: الصف 12 | الفصل الدراسي: 2

الدولة: المملكة العربية السعودية | المنهج: المنهج السعودي - وزارة التعليم

📚 معلومات الصفحة

الكتاب: كتاب الفيزياء - الصف 12 - الفصل 2 | المادة: الفيزياء | المرحلة: الصف 12 | الفصل الدراسي: 2

الدولة: المملكة العربية السعودية | المنهج: المنهج السعودي - وزارة التعليم

📄 النص الكامل للصفحة

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✅ حلول أسئلة الكتاب الرسمية

عدد الأسئلة: 7

سؤال 55: 55. وصل مصباحان مقاومة الأول $22 \Omega$ ومقاومة الثاني $4.5 \Omega$ على التوالي بمصدر فرق جهد مقداره $45 V$، كما هو موضح في الشكل 15-2. احسب مقدار: a. المقاومة المكافئة للدائرة. b. التيار المار في الدائرة. c. الهبوط في الجهد في كل مصباح. d. القدرة المستهلكة في كل مصباح.

الإجابة: س: 55 (a $R_{eq} = 26.5 \Omega$ $I \approx 1.70 A$ (b $V_{22} \approx 37.4 V$ (c $V_{4.5} \approx 7.64 V$ (d $P_{22} \approx 63.4 W$ $P_{4.5} \approx 13.0 W$

خطوات الحل:

  1. **الخطوة 1 (المعطيات):** لنحدد ما لدينا: - مقاومة المصباح الأول: $R_1 = 22 \Omega$ - مقاومة المصباح الثاني: $R_2 = 4.5 \Omega$ - فرق الجهد الكلي للمصدر: $V_{total} = 45 V$ المصباحان موصولان على التوالي.
  2. **الخطوة 2 (القوانين):** للدوائر الموصولة على التوالي: - المقاومة المكافئة: $R_{eq} = R_1 + R_2$ - قانون أوم: $V = I \times R$ - القدرة المستهلكة: $P = I^2 \times R$ أو $P = V \times I$ أو $P = V^2 / R$
  3. **الخطوة 3 (الحل):** **a. المقاومة المكافئة للدائرة:** بما أن المصباحين موصولان على التوالي، فإن المقاومة المكافئة هي مجموع مقاومتهما: $$R_{eq} = R_1 + R_2 = 22 \Omega + 4.5 \Omega = 26.5 \Omega$$ **b. التيار المار في الدائرة:** باستخدام قانون أوم للدائرة الكلية: $$I = \frac{V_{total}}{R_{eq}} = \frac{45 V}{26.5 \Omega} \approx 1.698 A$$ بالتقريب إلى منزلتين عشريتين: $I \approx 1.70 A$ **c. الهبوط في الجهد في كل مصباح:** نستخدم قانون أوم لكل مصباح على حدة، مع العلم أن التيار متساوٍ في جميع أجزاء دائرة التوالي: - الهبوط في الجهد عبر المصباح الأول ($R_1 = 22 \Omega$): $$V_1 = I \times R_1 = 1.698 A \times 22 \Omega \approx 37.356 V$$ بالتقريب إلى منزلة عشرية واحدة: $V_1 \approx 37.4 V$ - الهبوط في الجهد عبر المصباح الثاني ($R_2 = 4.5 \Omega$): $$V_2 = I \times R_2 = 1.698 A \times 4.5 \Omega \approx 7.641 V$$ بالتقريب إلى منزلتين عشريتين: $V_2 \approx 7.64 V$ **d. القدرة المستهلكة في كل مصباح:** نستخدم صيغة القدرة $P = I^2 \times R$ لكل مصباح: - القدرة المستهلكة في المصباح الأول ($R_1 = 22 \Omega$): $$P_1 = I^2 \times R_1 = (1.698 A)^2 \times 22 \Omega \approx 2.883 \times 22 \approx 63.426 W$$ بالتقريب إلى منزلة عشرية واحدة: $P_1 \approx 63.4 W$ - القدرة المستهلكة في المصباح الثاني ($R_2 = 4.5 \Omega$): $$P_2 = I^2 \times R_2 = (1.698 A)^2 \times 4.5 \Omega \approx 2.883 \times 4.5 \approx 12.9735 W$$ بالتقريب إلى منزلة عشرية واحدة: $P_2 \approx 13.0 W$
  4. **الخطوة 4 (النتائج):** a. المقاومة المكافئة للدائرة = **$26.5 \Omega$** b. التيار المار في الدائرة = **$1.70 A$** c. الهبوط في الجهد في المصباح الأول = **$37.4 V$**، والهبوط في الجهد في المصباح الثاني = **$7.64 V$** d. القدرة المستهلكة في المصباح الأول = **$63.4 W$**، والقدرة المستهلكة في المصباح الثاني = **$13.0 W$**

سؤال 56: 56. إذا كانت قراءة الفولتمتر الموضح في الشكل 16-2 تساوي $70.0 V$ فأجب عن الأسئلة الآتية: a. ما مقدار قراءة الأميتر؟ b. أي المقاومات أسخن؟ c. أي المقاومات أبرد؟ d. ما مقدار القدرة المزودة بواسطة البطارية؟

الإجابة: س: 56 (a $R_{tot} = 100 \Omega \Rightarrow$ $I = 0.70 A$ b) الأسخن: $50 \Omega$ c) الأبرد: $15 \Omega$ $P = 49 W$ (d

خطوات الحل:

  1. **الخطوة 1 (المعطيات):** لنحدد ما لدينا: - قراءة الفولتمتر (فرق الجهد الكلي للدائرة): $V_{total} = 70.0 V$ - المقاومات في الدائرة (من سياق السؤال والإجابة، نفترض أنها 15 \Omega و 35 \Omega و 50 \Omega موصولة على التوالي): $R_1 = 15 \Omega$, $R_2 = 35 \Omega$, $R_3 = 50 \Omega$.
  2. **الخطوة 2 (القوانين):** للدوائر الموصولة على التوالي: - المقاومة الكلية: $R_{tot} = R_1 + R_2 + R_3$ - قانون أوم: $I = V / R$ - القدرة المستهلكة: $P = I^2 \times R$ في دائرة التوالي، التيار المار في جميع المقاومات متساوٍ.
  3. **الخطوة 3 (الحل):** **a. ما مقدار قراءة الأميتر؟** أولاً، نحسب المقاومة الكلية للدائرة: $$R_{tot} = 15 \Omega + 35 \Omega + 50 \Omega = 100 \Omega$$ ثم نستخدم قانون أوم لحساب التيار الكلي المار في الدائرة (وهو قراءة الأميتر): $$I = \frac{V_{total}}{R_{tot}} = \frac{70.0 V}{100 \Omega} = 0.70 A$$ **b. أي المقاومات أسخن؟** القدرة المستهلكة (التي تتحول إلى حرارة) في المقاومة تُعطى بالعلاقة $P = I^2 \times R$. بما أن التيار $I$ متساوٍ لجميع المقاومات في دائرة التوالي، فإن المقاومة التي لها أكبر قيمة $R$ ستستهلك أكبر قدرة وتكون الأسخن. بمقارنة المقاومات: $15 \Omega$, $35 \Omega$, $50 \Omega$. المقاومة الأكبر هي $50 \Omega$. إذن، المقاومة الأسخن هي **$50 \Omega$**. **c. أي المقاومات أبرد؟** بالمنطق نفسه، المقاومة التي لها أقل قيمة $R$ ستستهلك أقل قدرة وتكون الأبرد. المقاومة الأصغر هي $15 \Omega$. إذن، المقاومة الأبرد هي **$15 \Omega$**. **d. ما مقدار القدرة المزودة بواسطة البطارية؟** القدرة الكلية المزودة بواسطة البطارية هي حاصل ضرب فرق الجهد الكلي في التيار الكلي: $$P_{total} = V_{total} \times I = 70.0 V \times 0.70 A = 49 W$$
  4. **الخطوة 4 (النتائج):** a. قراءة الأميتر = **$0.70 A$** b. المقاومة الأسخن = **$50 \Omega$** c. المقاومة الأبرد = **$15 \Omega$** d. القدرة المزودة بواسطة البطارية = **$49 W$**

سؤال 57: 57. إذا كان جهد البطارية الموضحة في الشكل 17-2 يساوي $110 V$، فأجب عن الأسئلة الآتية: a. ما مقدار قراءة الأميتر 1؟ b. ما مقدار قراءة الأميتر 2؟ c. ما مقدار قراءة الأميتر 3؟ d. ما مقدار قراءة الأميتر 4؟ e. أي المقاومات أسخن؟

الإجابة: س: 57 (a: $I_1 = 18.7 A$ $I_{20} = 5.50 A$ (b $I_{50} = 2.20 A$ (c $I_{10} = 11.0 A$ (d e) الأسخن $10 \Omega$، الأبرد $50 \Omega$

خطوات الحل:

  1. **الخطوة 1 (المعطيات):** لنحدد ما لدينا (بناءً على الشكل 17-2 الذي يمثل دائرة توازي): - جهد البطارية الكلي: $V_{battery} = 110 V$ - المقاومات في الفروع المتوازية: $R_{20} = 20 \Omega$, $R_{50} = 50 \Omega$, $R_{10} = 10 \Omega$. في دائرة التوازي، فرق الجهد عبر كل فرع يساوي جهد المصدر.
  2. **الخطوة 2 (القوانين):** للدوائر الموصولة على التوازي: - فرق الجهد عبر كل فرع: $V_{branch} = V_{battery}$ - قانون أوم: $I = V / R$ - التيار الكلي: $I_{total} = I_1 + I_2 + I_3 + ...$ - القدرة المستهلكة: $P = V^2 / R$ الأميتر 1 يقيس التيار الكلي. الأميتر 2 يقيس التيار المار في المقاومة $20 \Omega$. الأميتر 3 يقيس التيار المار في المقاومة $50 \Omega$. الأميتر 4 يقيس التيار المار في المقاومة $10 \Omega$.
  3. **الخطوة 3 (الحل):** **a. ما مقدار قراءة الأميتر 1؟** لقراءة الأميتر 1 (التيار الكلي)، نحتاج أولاً لحساب التيار في كل فرع. **b. ما مقدار قراءة الأميتر 2؟** الأميتر 2 يقيس التيار المار في المقاومة $20 \Omega$. فرق الجهد عبرها هو $110 V$. $$I_{20} = \frac{V_{battery}}{R_{20}} = \frac{110 V}{20 \Omega} = 5.50 A$$ **c. ما مقدار قراءة الأميتر 3؟** الأميتر 3 يقيس التيار المار في المقاومة $50 \Omega$. فرق الجهد عبرها هو $110 V$. $$I_{50} = \frac{V_{battery}}{R_{50}} = \frac{110 V}{50 \Omega} = 2.20 A$$ **d. ما مقدار قراءة الأميتر 4؟** الأميتر 4 يقيس التيار المار في المقاومة $10 \Omega$. فرق الجهد عبرها هو $110 V$. $$I_{10} = \frac{V_{battery}}{R_{10}} = \frac{110 V}{10 \Omega} = 11.0 A$$ الآن يمكننا حساب قراءة الأميتر 1 (التيار الكلي) بجمع التيارات في الفروع: $$I_1 = I_{total} = I_{20} + I_{50} + I_{10} = 5.50 A + 2.20 A + 11.0 A = 18.7 A$$ **e. أي المقاومات أسخن؟** القدرة المستهلكة (التي تتحول إلى حرارة) في المقاومة تُعطى بالعلاقة $P = V^2 / R$. بما أن فرق الجهد $V$ متساوٍ لجميع المقاومات في دائرة التوازي، فإن المقاومة التي لها أقل قيمة $R$ ستستهلك أكبر قدرة وتكون الأسخن. بمقارنة المقاومات: $20 \Omega$, $50 \Omega$, $10 \Omega$. المقاومة الأصغر هي $10 \Omega$. إذن، المقاومة الأسخن هي **$10 \Omega$**. وبالمثل، المقاومة الأكبر هي $50 \Omega$. إذن، المقاومة الأبرد هي **$50 \Omega$**.
  4. **الخطوة 4 (النتائج):** a. قراءة الأميتر 1 = **$18.7 A$** b. قراءة الأميتر 2 = **$5.50 A$** c. قراءة الأميتر 3 = **$2.20 A$** d. قراءة الأميتر 4 = **$11.0 A$** e. المقاومة الأسخن هي **$10 \Omega$**، والمقاومة الأبرد هي **$50 \Omega$**

سؤال 58: 58. إذا كانت قراءة الأميتر 3 الموضح في الشكل 17-2 تساوي $0.40 A$ فما مقدار: a. جهد البطارية؟ b. قراءة الأميتر 1؟ c. قراءة الأميتر 2؟ d. قراءة الأميتر 4؟

الإجابة: س: 58 (a $V = 20 V$ $I_1 = 3.4 A$ (b $I_{20} = 1.0 A$ (c $I_{10} = 2.0 A$ (d

خطوات الحل:

  1. **الخطوة 1 (المعطيات):** لنحدد ما لدينا (بناءً على الشكل 17-2 الذي يمثل دائرة توازي): - قراءة الأميتر 3 (التيار المار في المقاومة $50 \Omega$): $I_{50} = 0.40 A$ - المقاومات في الفروع المتوازية: $R_{20} = 20 \Omega$, $R_{50} = 50 \Omega$, $R_{10} = 10 \Omega$. في دائرة التوازي، فرق الجهد عبر كل فرع متساوٍ.
  2. **الخطوة 2 (القوانين):** للدوائر الموصولة على التوازي: - فرق الجهد عبر كل فرع: $V_{branch} = V_{battery}$ - قانون أوم: $V = I \times R$ - التيار الكلي: $I_{total} = I_1 + I_2 + I_3 + ...$ الأميتر 1 يقيس التيار الكلي. الأميتر 2 يقيس التيار المار في المقاومة $20 \Omega$. الأميتر 4 يقيس التيار المار في المقاومة $10 \Omega$.
  3. **الخطوة 3 (الحل):** **a. ما مقدار جهد البطارية؟** بما أن الأميتر 3 يقيس التيار المار في المقاومة $50 \Omega$، وهي موصولة على التوازي مع البطارية، فإن فرق الجهد عبر هذه المقاومة هو نفسه جهد البطارية. نستخدم قانون أوم: $$V_{battery} = I_{50} \times R_{50} = 0.40 A \times 50 \Omega = 20 V$$ الآن وقد عرفنا جهد البطارية ($20 V$)، يمكننا حساب التيارات في الفروع الأخرى. **c. ما مقدار قراءة الأميتر 2؟** الأميتر 2 يقيس التيار المار في المقاومة $20 \Omega$. فرق الجهد عبرها هو $20 V$. $$I_{20} = \frac{V_{battery}}{R_{20}} = \frac{20 V}{20 \Omega} = 1.0 A$$ **d. ما مقدار قراءة الأميتر 4؟** الأميتر 4 يقيس التيار المار في المقاومة $10 \Omega$. فرق الجهد عبرها هو $20 V$. $$I_{10} = \frac{V_{battery}}{R_{10}} = \frac{20 V}{10 \Omega} = 2.0 A$$ **b. ما مقدار قراءة الأميتر 1؟** الأميتر 1 يقيس التيار الكلي للدائرة، وهو مجموع التيارات في الفروع المتوازية: $$I_1 = I_{total} = I_{20} + I_{50} + I_{10} = 1.0 A + 0.40 A + 2.0 A = 3.4 A$$
  4. **الخطوة 4 (النتائج):** a. جهد البطارية = **$20 V$** b. قراءة الأميتر 1 = **$3.4 A$** c. قراءة الأميتر 2 = **$1.0 A$** d. قراءة الأميتر 4 = **$2.0 A$**

سؤال 59: 59. ما اتجاه التيار الاصطلاحي المار في المقاومة $50.0 \Omega$ الموضح في الشكل 17-2؟

الإجابة: س: 59: من أعلى المقاومة إلى أسفلها

خطوات الحل:

  1. **الشرح:** التيار الاصطلاحي يُعرف بأنه اتجاه تدفق الشحنات الموجبة، وهو يتدفق دائمًا من الطرف الموجب للبطارية إلى الطرف السالب عبر الدائرة الخارجية. في دائرة التوازي الموضحة في الشكل 17-2، يتم توصيل المقاومات بين نقطتين (أو سلكين) متوازيين يمثلان طرفي البطارية. إذا افترضنا أن السلك العلوي متصل بالطرف الموجب للبطارية والسلك السفلي متصل بالطرف السالب (وهو الترتيب الشائع في الرسومات)، فإن التيار الاصطلاحي سيتدفق من السلك العلوي (الجهد الأعلى) إلى السلك السفلي (الجهد الأقل) عبر كل مقاومة. لذلك، في المقاومة $50.0 \Omega$ (أو أي مقاومة أخرى في هذا الترتيب)، سيكون اتجاه التيار الاصطلاحي: **من أعلى المقاومة إلى أسفلها**.

سؤال 60: 60. إذا كان الحمل الموصول بطرفي بطارية يتكون من مقاومتين $15 \Omega$ و $47 \Omega$ موصولتين على التوالي فما مقدار: a. المقاومة الكلية للحمل؟ b. جهد البطارية إذا كان مقدار التيار المار في الدائرة $97 mA$؟

الإجابة: س: 60 (a $R_{tot} = 62 \Omega$ (b $V \approx 6.0 V$

خطوات الحل:

  1. **الخطوة 1 (المعطيات):** لنحدد ما لدينا: - مقاومة الحمل الأول: $R_1 = 15 \Omega$ - مقاومة الحمل الثاني: $R_2 = 47 \Omega$ - المقاومتان موصولتان على التوالي. - التيار المار في الدائرة: $I = 97 mA$
  2. **الخطوة 2 (القوانين):** للدوائر الموصولة على التوالي: - المقاومة الكلية: $R_{tot} = R_1 + R_2$ - قانون أوم: $V = I \times R$ يجب تحويل وحدات التيار من ملي أمبير (mA) إلى أمبير (A) قبل الحسابات: $1 A = 1000 mA$.
  3. **الخطوة 3 (الحل):** **a. ما مقدار المقاومة الكلية للحمل؟** بما أن المقاومتين موصولتان على التوالي، فإن المقاومة الكلية هي مجموع مقاومتهما: $$R_{tot} = R_1 + R_2 = 15 \Omega + 47 \Omega = 62 \Omega$$ **b. جهد البطارية إذا كان مقدار التيار المار في الدائرة $97 mA$؟** أولاً، نحول التيار من ملي أمبير إلى أمبير: $$I = 97 mA = 97 \times 10^{-3} A = 0.097 A$$ ثم نستخدم قانون أوم لحساب جهد البطارية: $$V = I \times R_{tot} = 0.097 A \times 62 \Omega = 6.014 V$$ بالتقريب إلى منزلة عشرية واحدة: $V \approx 6.0 V$
  4. **الخطوة 4 (النتائج):** a. المقاومة الكلية للحمل = **$62 \Omega$** b. جهد البطارية = **$6.0 V$**

سؤال 61: 61. أنوار الاحتفالات يتكون أحد أسلاك الزينة من 18 مصباحًا صغيرًا متماثلاً، موصولة على التوالي بمصدر جهد مقداره $120 V$. فإذا كان السلك يستنفد قدرة مقدارها $64 W$، فما مقدار: a. المقاومة المكافئة لسلك المصابيح؟ b. مقاومة كل مصباح؟ c. القدرة المستنفدة في كل مصباح؟

الإجابة: س: 61 (a: $R_{eq} = 225 \Omega$ $R_{lamp} = 12.5 \Omega$ (b $P_{lamp} \approx 3.6 W$ (c

خطوات الحل:

  1. **الخطوة 1 (المعطيات):** لنحدد ما لدينا: - عدد المصابيح: $N = 18$ مصباحًا متماثلاً. - نوع التوصيل: على التوالي. - مصدر الجهد الكلي: $V_{total} = 120 V$ - القدرة الكلية المستنفدة: $P_{total} = 64 W$
  2. **الخطوة 2 (القوانين):** للدوائر الموصولة على التوالي: - المقاومة المكافئة: $R_{eq} = N \times R_{lamp}$ (حيث $R_{lamp}$ هي مقاومة المصباح الواحد) - القدرة الكلية: $P_{total} = V_{total}^2 / R_{eq}$ أو $P_{total} = V_{total} \times I_{total}$ - القدرة المستنفدة في مصباح واحد: $P_{lamp} = P_{total} / N$ (لأن المصابيح متماثلة)
  3. **الخطوة 3 (الحل):** **a. المقاومة المكافئة لسلك المصابيح؟** نستخدم قانون القدرة الكلية بدلالة الجهد والمقاومة المكافئة: $$P_{total} = \frac{V_{total}^2}{R_{eq}}$$ بإعادة ترتيب المعادلة لإيجاد $R_{eq}$: $$R_{eq} = \frac{V_{total}^2}{P_{total}} = \frac{(120 V)^2}{64 W} = \frac{14400 V^2}{64 W} = 225 \Omega$$ **b. مقاومة كل مصباح؟** بما أن المصابيح متماثلة وموصولة على التوالي، فإن المقاومة المكافئة هي مجموع مقاوماتها الفردية. أي $R_{eq} = N \times R_{lamp}$. $$R_{lamp} = \frac{R_{eq}}{N} = \frac{225 \Omega}{18} = 12.5 \Omega$$ **c. القدرة المستنفدة في كل مصباح؟** بما أن المصابيح متماثلة، فإن القدرة الكلية المستنفدة تتوزع بالتساوي عليها: $$P_{lamp} = \frac{P_{total}}{N} = \frac{64 W}{18} \approx 3.555 W$$ بالتقريب إلى منزلة عشرية واحدة: $P_{lamp} \approx 3.6 W$
  4. **الخطوة 4 (النتائج):** a. المقاومة المكافئة لسلك المصابيح = **$225 \Omega$** b. مقاومة كل مصباح = **$12.5 \Omega$** c. القدرة المستنفدة في كل مصباح = **$3.6 W$**