صفحة 49 - 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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", "content_classification": "EDUCATIONAL_CONTENT", "has_instruction_words": false }, { "order": 10, "type": "main_content", "content": "مقلوب المقاومة المكافئة يساوي مجموع مقلوب المقاومات المفردة.", "content_classification": "EDUCATIONAL_CONTENT", "has_instruction_words": false }, { "order": 11, "type": "main_content", "content": "ويمكن استخدام هذه المعادلة لإيجاد المقاومة المكافئة لأي عدد من المقاومات على التوازي.", "content_classification": "EDUCATIONAL_CONTENT", "has_instruction_words": false }, { "order": 12, "type": "header", "content": "تجربة", "content_classification": "EDUCATIONAL_CONTENT" }, { "order": 13, "type": "header", "content": "مقاومة التوازي", "content_classification": "EDUCATIONAL_CONTENT" }, { "order": 14, "type": "main_content", "content": "ركب دائرة كهربائية تتكون من مصدر قدرة، ومقاومة، وأميتر.", "content_classification": "QUESTION_ACTIVITY", "question_indicators": { "has_question_words": false, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "open_ended" }, { "order": 15, "type": "exercise", "title": "1", "content": "توقع ماذا يحدث للتيار في الدائرة الكهربائية عند توصيل مقاومة أخرى مماثلة على التوازي.", "content_classification": "QUESTION_ACTIVITY", "question_indicators": { "has_question_words": true, "has_numbering": true, "question_number": "1", "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "open_ended" }, { "order": 16, "type": "exercise", "title": "2", "content": "اختبر توقعك.", "content_classification": "QUESTION_ACTIVITY", "question_indicators": { "has_question_words": false, "has_numbering": true, "question_number": "2", "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "open_ended" }, { "order": 17, "type": "main_content", "content": "توقع مقداري التيارين إذا تضمنت الدائرة ثلاث أو أربع مقاومات متماثلة موصولة على التوازي.", 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false, "has_instruction_words": true }, "format": "open_ended" }, { "order": 21, "type": "exercise", "title": "5", "content": "فسّر نتائجك بتضمينها كيفية تغير المقاومة.", "content_classification": "QUESTION_ACTIVITY", "question_indicators": { "has_question_words": true, "has_numbering": true, "question_number": "5", "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "open_ended" }, { "order": 22, "type": "main_content", "content": "تكملة النص في العمود الأيسر", "content_classification": "EDUCATIONAL_CONTENT", "has_instruction_words": false }, { "order": 23, "type": "main_content", "content": "تكملة النص في العمود الأيسر", "content_classification": "EDUCATIONAL_CONTENT", "has_instruction_words": false }, { "order": 24, "type": "main_content", "content": "تكملة النص في العمود الأيسر", "content_classification": "EDUCATIONAL_CONTENT", "has_instruction_words": false }, { "order": 25, "type": "main_content", "content": "تكملة النص في العمود 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"content_classification": "EDUCATIONAL_CONTENT", "has_instruction_words": false }

✅ حلول أسئلة الكتاب الرسمية

عدد الأسئلة: 6

سؤال 1: 1. توقع ماذا يحدث للتيار في الدائرة الكهربائية عند توصيل مقاومة أخرى مماثلة للمقاومة الأولى على التوازي معه؟

الإجابة: س1: يزداد التيار الكلي (يتضاعف تقريبًا)، لأن المقاومة المكافئة تقل للنصف.

خطوات الحل:

  1. **الخطوة 1 (المفهوم):** عند توصيل مقاومتين على التوازي، فإن المقاومة الكلية المكافئة للدائرة تقل. إذا كانت المقاومتان متماثلتين، فإن المقاومة المكافئة تقل إلى النصف تقريباً.
  2. **الخطوة 2 (التطبيق):** وفقاً لقانون أوم ($I = \frac{V}{R}$)، إذا قلت المقاومة الكلية للدائرة (R) بينما يظل فرق الجهد (V) ثابتاً (بافتراض مصدر جهد ثابت)، فإن التيار الكلي (I) سيزداد.
  3. **الخطوة 3 (النتيجة):** لذلك، عند توصيل مقاومة أخرى مماثلة على التوازي، **يزداد التيار الكلي في الدائرة (ويتضاعف تقريباً)** لأن المقاومة المكافئة تقل للنصف.

سؤال 2: 2. اختبر توقعك.

الإجابة: س2: يزداد التيار الكلي (ضعف قيمته) بينما تيار كل فرع متساوي.

خطوات الحل:

  1. **الخطوة 1 (تأكيد التوقع):** بالفعل، عند توصيل مقاومة أخرى مماثلة على التوازي، يزداد التيار الكلي في الدائرة.
  2. **الخطوة 2 (تيار الفروع):** في الدوائر المتوازية، يتوزع التيار الكلي على الفروع. بما أن المقاومتين متماثلتان، فإن التيار سيتوزع بالتساوي بينهما. وبالتالي، فإن تيار كل فرع سيبقى كما لو كانت مقاومة واحدة، بينما التيار الكلي هو مجموع تيارات الفروع.
  3. **الخطوة 3 (النتيجة):** إذن، **يزداد التيار الكلي (ليصبح ضعف قيمته الأصلية تقريباً)، بينما يظل تيار كل فرع متساوياً** (أي يمر نفس التيار في كل مقاومة على حدة كما لو كانت منفردة).

سؤال 3: 3. توقع مقداري التيارين إذا تضمنت الدائرة ثلاث أو أربع مقاومات متماثلة موصولة على التوازي.

الإجابة: س3: عند 3 مقاومات: $R_{eq} = \frac{R}{3}, I_{tot} = 3I_1$ عند 4 مقاومات: $R_{eq} = \frac{R}{4}, I_{tot} = 4I_1$

خطوات الحل:

  1. **الخطوة 1 (المعطيات والمفاهيم):** لنفترض أن لدينا مقاومات متماثلة، قيمة كل منها R. عند توصيل 'n' من هذه المقاومات على التوازي، فإن المقاومة المكافئة ($R_{eq}$) تُعطى بالعلاقة: $$R_{eq} = \frac{R}{n}$$
  2. **الخطوة 2 (حساب التيار الكلي):** بافتراض أن فرق الجهد عبر الدائرة ثابت (V)، فإن التيار الكلي ($I_{tot}$) يُحسب من قانون أوم: $$I_{tot} = \frac{V}{R_{eq}} = \frac{V}{\frac{R}{n}} = n \times \frac{V}{R}$$ إذا كان $I_1 = \frac{V}{R}$ هو التيار المار في مقاومة واحدة، فإن $I_{tot} = n \times I_1$.
  3. **الخطوة 3 (توقع التيارات):** - **عند 3 مقاومات متماثلة على التوازي:** المقاومة المكافئة: $$R_{eq} = \frac{R}{3}$$ التيار الكلي: $$I_{tot} = 3 \times I_1$$ - **عند 4 مقاومات متماثلة على التوازي:** المقاومة المكافئة: $$R_{eq} = \frac{R}{4}$$ التيار الكلي: $$I_{tot} = 4 \times I_1$$ إذن، الإجابة هي: **عند 3 مقاومات: $R_{eq} = \frac{R}{3}, I_{tot} = 3I_1$؛ عند 4 مقاومات: $R_{eq} = \frac{R}{4}, I_{tot} = 4I_1$**

سؤال 4: 4. اختبر توقعك.

الإجابة: س4: يزداد التيار الكلي بزيادة عدد المقاومات (3 أضعاف، 4 أضعاف) وتيار الفرع ثابت.

خطوات الحل:

  1. **الخطوة 1 (تأكيد التوقع):** عند زيادة عدد المقاومات المتماثلة الموصولة على التوازي، تزداد المسارات التي يمكن للتيار أن يسلكها، مما يؤدي إلى انخفاض المقاومة الكلية للدائرة.
  2. **الخطوة 2 (تأثير على التيار الكلي وتيار الفرع):** بما أن المقاومة الكلية تقل، فإن التيار الكلي يزداد (3 أضعاف عند 3 مقاومات، 4 أضعاف عند 4 مقاومات، وهكذا). ومع ذلك، بما أن كل مقاومة موصولة مباشرة بمصدر الجهد، فإن فرق الجهد عبر كل مقاومة يبقى ثابتاً، وبالتالي فإن التيار المار في كل فرع (تيار الفرع) يظل ثابتاً.
  3. **الخطوة 3 (النتيجة):** إذن، **يزداد التيار الكلي بزيادة عدد المقاومات (3 أضعاف، 4 أضعاف)، بينما يظل تيار الفرع ثابتاً**.

سؤال 5: 5. أنشئ جدول بيانات لتوضيح النتائج.

الإجابة: س5: الجدول: 1: $R, I_1, I_1$ 2: $\frac{R}{2}, I_1, 2I_1$ 3: $\frac{R}{3}, I_1, 3I_1$ 4: $\frac{R}{4}, I_1, 4I_1$

خطوات الحل:

  1. **الخطوة 1 (تحديد المتغيرات):** لتوضيح النتائج، نحتاج إلى جدول يربط بين عدد المقاومات الموصولة على التوازي، المقاومة المكافئة، التيار المار في كل فرع (تيار الفرع)، والتيار الكلي للدائرة.
  2. **الخطوة 2 (بناء الجدول):** بافتراض أن المقاومة الواحدة هي R، والتيار المار فيها بمفردها هو $I_1$ (حيث $I_1 = \frac{V}{R}$)، يمكننا إنشاء الجدول التالي: | عدد المقاومات (n) | المقاومة المكافئة ($R_{eq}$) | تيار الفرع ($I_{branch}$) | التيار الكلي ($I_{tot}$) | |-------------------|-------------------------------|-----------------------------|---------------------------| | 1 | R | $I_1$ | $I_1$ | | 2 | $\frac{R}{2}$ | $I_1$ | $2I_1$ | | 3 | $\frac{R}{3}$ | $I_1$ | $3I_1$ | | 4 | $\frac{R}{4}$ | $I_1$ | $4I_1$ |
  3. **الخطوة 3 (النتيجة):** هذا الجدول يوضح كيف تتغير المقاومة المكافئة والتيار الكلي مع زيادة عدد المقاومات المتماثلة الموصولة على التوازي، مع بقاء تيار الفرع ثابتاً.

سؤال 6: 6. فسّر نتائجك بتضمينها كيفية تغير المقاومة.

الإجابة: س6: تقل المقاومة لزيادة المسارات ($R_{eq} = \frac{R}{n}$)، فيزداد التيار الكلي ($I = \frac{V}{R_{eq}}$) وتيار الفروع ثابت.

خطوات الحل:

  1. **الشرح:** عند توصيل المقاومات على التوازي، فإننا نوفر مسارات إضافية لتدفق التيار الكهربائي. كلما زاد عدد هذه المسارات، كلما أصبح تدفق التيار أسهل، وهذا يعني أن المقاومة الكلية المكافئة للدائرة تقل. يمكن التعبير عن ذلك بالعلاقة: $R_{eq} = \frac{R}{n}$، حيث R هي قيمة المقاومة الواحدة و n هو عدد المقاومات المتماثلة. وفقاً لقانون أوم ($I = \frac{V}{R_{eq}}$)، بما أن فرق الجهد (V) عبر الدائرة يظل ثابتاً (بافتراض مصدر جهد ثابت)، فإن أي نقصان في المقاومة المكافئة ($R_{eq}$) سيؤدي حتماً إلى زيادة في التيار الكلي ($I_{tot}$) المار في الدائرة. أما بالنسبة لتيار الفروع، فبما أن كل مقاومة موصولة مباشرة بمصدر الجهد، فإن فرق الجهد عبر كل مقاومة يبقى ثابتاً ومساوياً لجهد المصدر. ولأن المقاومات متماثلة، فإن التيار المار في كل فرع ($I_{branch} = \frac{V}{R}$) يظل ثابتاً ولا يتغير بزيادة عدد المقاومات الموصولة على التوازي. لذلك، **تقل المقاومة الكلية لزيادة المسارات المتاحة للتيار ($R_{eq} = \frac{R}{n}$)، فيزداد التيار الكلي ($I_{tot} = \frac{V}{R_{eq}}$)، بينما يظل تيار الفروع ثابتاً**.