রোধ (পাঠ ৪ ও ৫)

অষ্টম শ্রেণি (দাখিল) - বিজ্ঞান বর্তনী ও চলবিদ্যুৎ | - | NCTB BOOK

বিদ্যুৎ প্রবাহ তৈরি হয় ইলেকট্রনের প্রবাহের জন্য। কোনো পরিবাহীর দুই প্রান্তে বিভব পার্থক্য থাকলে এই প্রবাহ শুরু হয়। এক্ষেত্রে ইলেকট্রন নিম্ন বিভব থেকে উচ্চ বিভবের দিকে প্রবাহিত হয়। এই ইলেকট্রন স্রোত পরিবাহীর মধ্য দিয়ে চলার সময় পরিবাহীর অভ্যন্তরস্থ অণু-পরমাণুর সাথে সংঘর্ষে লিপ্ত হয়। ফলে এর গতি বাধাপ্রাপ্ত হয় এবং বিদ্যুৎ প্রবাহও বিঘ্নিত হয়। পরিবাহীর এই বাধাদানের ধর্ম হলো রোধ। মূলত, পরিবাহীর যে ধর্মের জন্য এর মধ্য দিয়ে বিদ্যুৎ চলাচল বাধাগ্রস্ত হয় তাই হলো রোধ।

ও'মের সূত্র
কোনো পরিবাহীর মধ্য দিয়ে তড়িৎ প্রবাহিত হবে কিনা তা নির্ভর করছে ঐ পরিবাহীর দুই প্রান্তের বিভব পার্থক্যের উপর। এছাড়াও পরিবাহীর আকৃতি ও উপাদান এমনকি পরিবাহীর তাপমাত্রার উপরও এর তড়িৎ প্রবাহের মাত্রা নির্ভর করে। তাপমাত্রা যদি স্থির রাখা যায় তবে নির্দিষ্ট পরিবাহীর মধ্য দিয়ে তড়িৎ প্রবাহ শুধুমাত্র এর দুই প্রান্তের বিভব পার্থক্যের উপর নির্ভর করে। নির্দিষ্ট তাপমাত্রায় কোনো পরিবাহীর দুই প্রান্তের বিভব পার্থক্য ও এর মধ্য দিয়ে প্রবাহিত তড়িৎ প্রবাহের অনুপাত থেকে ঐ তাপমাত্রায় ঐ পরিবাহীর রোধ পরিমাপ করা হয়। এছাড়া নির্দিষ্ট তাপমাত্রায় নির্দিষ্ট আকৃতির একটি পরিবাহীর মধ্য দিয়ে তড়িৎপ্রবাহ এর দুই প্রান্তের সাথে বিভব পার্থক্য একটি নিয়ম মেনে চলে। এই নিয়মটির জন্য জর্জ সাইমন ও'মের (১৭৮৩–১৮৫৪) একটি সূত্র প্রণয়ন করেন, যা ও'মের সূত্র নামে পরিচিত।

ও'মের সূত্র : তাপমাত্রা স্থির থাকলে কোনো নির্দিষ্ট পরিবাহীর মধ্য দিয়ে প্রবাহিত তড়িৎ প্রবাহের মান পরিবাহীর দুই প্রান্তের বিভব পার্থক্যের মানের সমানুপাতিক।

ও'মের সূত্র থেকে এটা সহজেই বলা যায় যে, পরিবাহীর দুই প্রান্তের বিভব পার্থক্য বেশি থাকলে তড়িৎ প্রবাহের মাত্রা বেশি হবে। আবার এই বিভব পার্থক্য কম থাকলে তড়িৎ প্রবাহ কম হবে (চিত্র ৯.৪)।

কোনো পরিবাহীর দুই প্রান্তের বিভব পার্থক্য V, এর রোধ R এবং তড়িৎ প্রবাহ I হলে

চিত্র ৯.৪ : ও'মের সূত্রের লেখচিত্র

 

তড়িৎ প্রবাহ, I=VR

সুতরাং কোনো নির্দিষ্ট পরিবাহীর মধ্য দিয়ে প্রবাহিত তড়িৎ প্রবাহ পরিবাহীর নিজস্ব রোধের ব্যস্তানুপাতিক।

রোধের একক
রোধের এস আই একক হলো ও'ম। কোনো পরিবাহীর দুই প্রান্তের বিভব পার্থক্য ১ ভোল্ট এবং এর মধ্য দিয়ে প্রবাহিত তড়িৎ প্রবাহ ১ অ্যাম্পিয়ার হলে, ঐ পরিবাহীর রোধ হবে ১ ও'ম।

common.content_added_by
টপ রেটেড অ্যাপ

স্যাট অ্যাকাডেমী অ্যাপ

আমাদের অল-ইন-ওয়ান মোবাইল অ্যাপের মাধ্যমে সীমাহীন শেখার সুযোগ উপভোগ করুন।

ভিডিও
লাইভ ক্লাস
এক্সাম
ডাউনলোড করুন
Promotion
Request history8.2.27PHP Version145msRequest Duration36MBMemory UsageGET academy/{slug}Route
    • Booting (87.96ms)time
    • Application (57.18ms)time
    • 1 x Booting (60.6%)
      87.96ms
      1 x Application (39.4%)
      57.18ms
      52 templates were rendered
      • 1x academy.subject.read_chapterread_chapter.blade.php#?blade
      • 1x academy.include.sidebarListsidebarList.blade.php#?blade
      • 1x academy.include.left_sidebar_menuleft_sidebar_menu.blade.php#?blade
      • 14x academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • 1x common.modal.self_test_modalself_test_modal.blade.php#?blade
      • 1x common.modal.bookmark_modalbookmark_modal.blade.php#?blade
      • 1x common.modal.error_report_modalerror_report_modal.blade.php#?blade
      • 1x common.modal.video_modalvideo_modal.blade.php#?blade
      • 1x common.script.page_type_scriptpage_type_script.blade.php#?blade
      • 1x job.job_include.job_scriptjob_script.blade.php#?blade
      • 1x common.script.activity_scriptactivity_script.blade.php#?blade
      • 1x common.script.test_scripttest_script.blade.php#?blade
      • 1x common.script.custom_dropdowncustom_dropdown.blade.php#?blade
      • 1x common.script.follow_unfollow_scriptfollow_unfollow_script.blade.php#?blade
      • 1x common.script.short_statistics_scriptshort_statistics_script.blade.php#?blade
      • 1x common.script.navigator_sharenavigator_share.blade.php#?blade
      • 1x layouts.satt-appsatt-app.blade.php#?blade
      • 1x includes.header_link2header_link2.blade.php#?blade
      • 1x laravelpwa::metameta.blade.php#?blade
      • 1x layouts.headerheader.blade.php#?blade
      • 1x layouts.toolbartoolbar.blade.php#?blade
      • 1x frontend.downloadourappdownloadourapp.blade.php#?blade
      • 1x frontend.referralreferral.blade.php#?blade
      • 1x auth.user_type_modaluser_type_modal.blade.php#?blade
      • 1x layouts.footerfooter.blade.php#?blade
      • 1x common.login_modallogin_modal.blade.php#?blade
      • 1x components.authentication-card-logoauthentication-card-logo.blade.php#?blade
      • 1x common.includes.promotion_modalpromotion_modal.blade.php#?blade
      • 1x common.includes.notification_item_modalnotification_item_modal.blade.php#?blade
      • 1x common.includes.notification_item_list_modalnotification_item_list_modal.blade.php#?blade
      • 1x common.includes.promotion_offcanvaspromotion_offcanvas.blade.php#?blade
      • 1x includes.footer_link2footer_link2.blade.php#?blade
      • 1x includes.restrictrestrict.blade.php#?blade
      • 1x livewire-alert::components.scriptsscripts.blade.php#?blade
      • 1x livewire-alert::components.flashflash.blade.php#?blade
      • 1x admin.include.toastrtoastr.blade.php#?blade
      • 1x common.search.search_scriptsearch_script.blade.php#?blade
      • 1x common.script.promotion_scriptpromotion_script.blade.php#?blade
      • 1x common.script.promotion_functionspromotion_functions.blade.php#?blade
      uri
      GET academy/{slug}
      middleware
      web, throttle:global
      controller
      App\Http\Controllers\Academy\SubjectController@chapter
      namespace
      prefix
      where
      as
      academy.subject.chapter
      file
      app/Http/Controllers/Academy/SubjectController.php:102-110
      20 statements were executed (2 duplicates)Show only duplicates21.27ms
      • SubjectRepository.php#89debugerror_satt1.9msselect `id`, `main_category_id`, `parent_id`, `show_content` from `subjects` where `slug` = 'রোধ-76742' and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: রোধ-76742
        Backtrace
        • app/Repositories/SubjectRepository.php:89
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:86
        • app/Services/SubjectService.php:23
      • SubjectService.php#34debugerror_satt400μsupdate `subjects` set `view_count` = `view_count` + 1, `subjects`.`updated_at` = '2025-03-13 06:05:51' where `id` = 19877
        Bindings
        • 0: 2025-03-13 06:05:51
        • 1: 19877
        Backtrace
        • app/Services/SubjectService.php:34
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
        • vendor/laravel/framework/src/Illuminate/Routing/Route.php:266
      • QueryBuilder.php#38debugerror_satt230μsselect `_lft`, `_rgt` from `subjects` where `id` = 19877 limit 1
        Bindings
        • 0: 19877
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:38
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:60
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:235
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:227
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
      • QueryBuilder.php#305debugerror_satt180μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `show_content`, `num_of_mcq`, `num_of_written`, `des_added_by`, `des_updated_by`, `author_name`, `link_subject_id`, `sub_category_id`, `main_category_id`, `slug`, `meta_og_title`, `meta_keyword`, `meta_description`, `vote`, `view_count`, `icon`, `page_type`, `chapter_name` from `subjects` where (`subjects`.`_lft` between 50573 and 50574) and `subjects`.`deleted_at` is null
        Bindings
        • 0: 50573
        • 1: 50574
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt140μsselect `id`, `description`, `short_description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (19877) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt120μsselect `id`, `name`, `slug` from `sub_categories` where `sub_categories`.`id` in (4874) and `sub_categories`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt200μsselect `id`, `user_id`, `completeable_type`, `completeable_id`, `complete_progress`, `is_complete` from `completes` where `completes`.`completeable_id` in (19877) and `completes`.`completeable_type` = 'App\\Models\\Subject'
        Bindings
        • 0: App\Models\Subject
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt110μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `show_content`, `des_added_by`, `des_updated_by`, `author_name`, `link_subject_id` from `subjects` where `subjects`.`id` in (12418) and `subjects`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt160μsselect `id`, `description`, `short_description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (12418) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt110μsselect `id`, `name`, `avatar` from `users` where `users`.`id` in (38332) and `users`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt250μsselect * from (select `questions`.`id`, `questions`.`subject_id`, `questions`.`category_id`, `questions`.`sub_category_id`, `questions`.`board_exam_id`, `questions`.`passage_id`, `questions`.`question_type`, `questions`.`question`, `questions`.`is_duplicate`, `questions`.`status`, `questions`.`image`, `subjectables`.`subject_id` as `pivot_subject_id`, `subjectables`.`subjectable_id` as `pivot_subjectable_id`, `subjectables`.`subjectable_type` as `pivot_subjectable_type`, row_number() over (partition by `subjectables`.`subject_id` order by `questions`.`created_at` desc) as `laravel_row` from `questions` inner join `subjectables` on `questions`.`id` = `subjectables`.`subjectable_id` where `subjectables`.`subject_id` in (19877) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `questions`.`status` = 'active' and `questions`.`deleted_at` is null) as `laravel_table` where `laravel_row` <= 5 order by `laravel_row`
        Bindings
        • 0: App\Models\Question
        • 1: active
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • SubjectRepository.php#117debugerror_satt200μsselect * from `subjects` where `subjects`.`id` = 19877 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 19877
        Backtrace
        • app/Repositories/SubjectRepository.php:117
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:116
        • app/Services/SubjectService.php:51
      • SubjectRepository.php#120debugerror_satt8.75msselect `id`, `name`, `slug`, `parent_id`, `_lft`, `_rgt` from `subjects` where (50574 between `subjects`.`_lft` and `subjects`.`_rgt` and `subjects`.`id` <> 19877) and `subjects`.`deleted_at` is null order by `_lft` asc
        Bindings
        • 0: 50574
        • 1: 19877
        Backtrace
        • app/Repositories/SubjectRepository.php:120
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:116
        • app/Services/SubjectService.php:51
      • SubjectRepository.php#132debugerror_satt160μsselect * from `subjects` where `subjects`.`id` = 19877 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 19877
        Backtrace
        • app/Repositories/SubjectRepository.php:132
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:131
        • app/Services/SubjectService.php:52
      • SubjectRepository.php#135debugerror_satt110μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `slug`, `meta_og_title`, `meta_keyword`, `meta_description` from `subjects` where `subjects`.`id` = 19872 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 19872
        Backtrace
        • app/Repositories/SubjectRepository.php:135
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:131
        • app/Services/SubjectService.php:52
      • SubjectRepository.php#135debugerror_satt110μsselect `id`, `description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (19872) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • app/Repositories/SubjectRepository.php:135
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:131
        • app/Services/SubjectService.php:52
      • SubjectRepository.php#320debugerror_satt200μsselect * from `mediables` where `mediable_type` = 'App\\Models\\Subject' and `mediable_id` in (19877)
        Bindings
        • 0: App\Models\Subject
        • 1: 19877
        Backtrace
        • app/Repositories/SubjectRepository.php:320
        • app/Services/SubjectService.php:67
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
      • SubjectRepository.php#335debugerror_satt190μsselect `videos`.`video_src_url`, `mediables`.`mediable_id` as `chapter_id` from `videos` inner join `mediables` on `mediables`.`mediable_id` = `videos`.`id` where `videos`.`id` = 0 and `videos`.`video_src` = 'youtube' and `videos`.`deleted_at` is null
        Bindings
        • 0: 0
        • 1: youtube
        Backtrace
        • app/Repositories/SubjectRepository.php:335
        • app/Services/SubjectService.php:68
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
      • SubjectService.php#73debugerror_satt7.55msselect `id`, `name`, `main_category_id`, `slug` from `subjects` where `id` <> 19877 and `parent_id` = 19872 and `main_category_id` = 2 and `subjects`.`deleted_at` is null limit 5
        Bindings
        • 0: 19877
        • 1: 19872
        • 2: 2
        Backtrace
        • app/Services/SubjectService.php:73
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
        • vendor/laravel/framework/src/Illuminate/Routing/Route.php:266
      • restrict.blade.php#30debugerror_satt200μsselect * from `package_plans` where `status` = 'active' and `package_plans`.`deleted_at` is null
        Bindings
        • 0: active
        Backtrace
        • view::includes.restrict:30
        • vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • vendor/livewire/livewire/src/Mechanisms/ExtendBlade/ExtendedCompilerEngine.php:22
        • vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:75
      App\Models\Subject
      13Subject.php#?
      App\Models\PackagePlan
      4PackagePlan.php#?
      App\Models\SubjectDescription
      3SubjectDescription.php#?
      App\Models\SubCategory
      1SubCategory.php#?
      App\Models\User
      1User.php#?
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          path_info
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          status_code
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          status_text
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          ClearShow all
          Date ↕MethodURLData
          #12025-03-13 06:05:51GET/academy/%E0%A6%B0%E0%A7%8B%E0%A6%A7-76742522022