יחס הפוך

יחס הפוךאנגלית: Inverse Proportion) בין שני משתנים מתקיים כאשר מכפלתם קבועה. במקרה כזה משתנה אחד נמצא ביחס ישר להופכי של המשתנה האחר. כלומר: כאשר הוא קבוע כלשהו. כאשר מתקיים יחס הפוך בין שני משתנים, משתנה אחד קטן ככל שהמשתנה האחר גדל.

דוגמה: כאשר מחלקים עוגה שווה בשווה בין משתתפים אחדים, גודל הפרוסה נמצא ביחס הפוך למספר המשתתפים. אם נסמן ב-N את מספר המשתתפים, ב-m את משקל העוגה בק"ג, אזי כל משתתף יקבל פרוסה P שמשקלה ק"ג. במקרה זה, קיים יחס הפוך בין P (גודל הפרוסה) ל-N (מספר המשתתפים) והקבוע הוא m (גודל העוגה). דוגמה נוספת: אם אדם חפץ מאוד בדבר כלשהו, הימנעותו ממגע עם אותו דבר בו הוא חפץ נמצא ביחס הפוך לרצונו.

דוגמאות ליחס הפוך במדע

  • כשמופעל על גוף כוח קבוע F, התאוצה a של הגוף נמצאת ביחס הפוך למסה m שלו:
  • גודל הלחץ P נמצא ביחס הפוך ביחס לגודל השטח A שעליו פועל כוח:
  • בתהליך איזותרמי, מכפלת הלחץ P והנפח V חייבת להישאר קבועה:
  • בחוק וין:
  • לפי חוק אוהם, בהינתן מקור מתח קבוע (כמו למשל בשקע חשמלי ביתי), הזרם נמצא ביחס הפוך להתנגדות:

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