Ejercicios de teorema de Tellegen en redes eléctricas, Monografías, Ensayos de Análisis de Circuitos Electrónicos

¡Descarga Ejercicios de teorema de Tellegen en redes eléctricas y más Monografías, Ensayos en PDF de Análisis de Circuitos Electrónicos solo en Docsity! 𝑃𝑃12𝑉𝑉 = (−12) ∗ (2) = −24 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟐𝟐𝟐𝟐 𝑾𝑾 𝑃𝑃1 = (4) ∗ (2) = 8 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟖𝟖 𝑾𝑾 𝑃𝑃2𝑣𝑣𝑣𝑣 = (−2𝑉𝑉𝑣𝑣) ∗ (2) = −4𝑉𝑉𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟐𝟐𝑉𝑉𝑣𝑣𝑊𝑊 𝑃𝑃2 = (𝑉𝑉𝑣𝑣) ∗ (2) = 2𝑉𝑉𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟐𝟐𝑉𝑉𝑣𝑣𝑊𝑊 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑃𝑃𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑎𝑎 24 + 4𝑉𝑉𝑣𝑣 = 8 + 2𝑉𝑉𝑣𝑣 𝑉𝑉𝑣𝑣 = −8 𝑣𝑣 𝑃𝑃2 = (−8) ∗ (2) = −16 𝑊𝑊 → 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 16 𝑊𝑊 𝑃𝑃36𝑉𝑉 = (−36) ∗ 𝐼𝐼𝑣𝑣 = −36𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 36𝐼𝐼𝑣𝑣 𝑊𝑊 𝑃𝑃1 = (12) ∗ 𝐼𝐼𝑣𝑣 = 12𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 12𝐼𝐼𝑣𝑣 𝑊𝑊 𝑃𝑃2 = (24) ∗ 2 = 48 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 48 𝑊𝑊 𝑃𝑃1𝐼𝐼𝑥𝑥 = (−1𝐼𝐼𝑣𝑣) ∗ 2 = −2𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 2𝐼𝐼𝑣𝑣 𝑊𝑊 𝑃𝑃3 = (28) ∗ 2 = 56 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 56 𝑊𝑊 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑃𝑃𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑎𝑎 36𝐼𝐼𝑣𝑣 + 2𝐼𝐼𝑣𝑣 = 12𝐼𝐼𝑣𝑣 + 48 + 56 𝐼𝐼𝑣𝑣 = 4𝐴𝐴 𝑃𝑃36𝑉𝑉 = (−36) ∗ 𝐼𝐼𝑣𝑣 = −36𝐼𝐼𝑣𝑣𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 36𝐼𝐼𝑣𝑣𝑊𝑊 𝑃𝑃1 = (12) ∗ 𝐼𝐼𝑣𝑣 = 12𝐼𝐼𝑣𝑣𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 12𝐼𝐼𝑣𝑣𝑊𝑊 𝑃𝑃2𝐼𝐼𝑥𝑥 = (24) ∗ 2𝐼𝐼𝑣𝑣 = 48𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 48𝐼𝐼𝑣𝑣 𝑊𝑊 𝑃𝑃2 = (−8) ∗ 2 = −16 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 16 𝑊𝑊 𝑃𝑃3 = (−16) ∗ 2 = −32 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 32 𝑊𝑊 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑃𝑃𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑎𝑎 361𝐼𝐼𝑣𝑣 + 16 + 32 = 12𝐼𝐼𝑣𝑣 + 48𝐼𝐼𝑣𝑣 𝐼𝐼𝑣𝑣 = 2𝐴𝐴 𝑃𝑃1 = (12) ∗ (2) = 24𝑊𝑊 𝑃𝑃18𝑉𝑉 = (−18) ∗ 𝐼𝐼𝑣𝑣 = −18𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟏𝟏𝟖𝟖𝑰𝑰𝒙𝒙 𝑾𝑾 𝑃𝑃1 = (−6) ∗ 𝐼𝐼𝑣𝑣 = −6𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟔𝟔𝑰𝑰𝒙𝒙 𝑾𝑾 𝑃𝑃24𝑉𝑉 = (−24) ∗ 2 = −48 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟐𝟐𝟖𝟖𝑾𝑾 𝑃𝑃2 = (4) ∗ 2𝐼𝐼𝑣𝑣 = 8𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟖𝟖𝑰𝑰𝒙𝒙 𝑾𝑾 𝑃𝑃2𝐼𝐼𝑥𝑥 = (20) ∗ 2𝐼𝐼𝑣𝑣 = 40𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟐𝟐𝟒𝟒𝑰𝑰𝒙𝒙 𝑾𝑾 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑃𝑃𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑎𝑎 18𝐼𝐼𝑣𝑣 + 6𝐼𝐼𝑣𝑣 + 48 = 8𝐼𝐼𝑣𝑣 + 40𝐼𝐼𝑣𝑣 𝐼𝐼𝑣𝑣 = 2𝐴𝐴 48 + 24 = 18 + 24 + 2𝑉𝑉𝑣𝑣 + 32 𝑉𝑉𝑣𝑣 = −1𝑉𝑉 𝑃𝑃24𝑉𝑉 = (−24) ∗ 2 = −48 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟐𝟐𝟖𝟖 𝑾𝑾 𝑃𝑃4𝑉𝑉 = (4) ∗ 2 = 8 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 8 𝑊𝑊 𝑃𝑃8𝑉𝑉 = (8) ∗ 2 = 16 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 16 𝑊𝑊 𝑃𝑃2𝐴𝐴 = (−12) ∗ 2 = −24 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟐𝟐𝟐𝟐 𝑾𝑾 𝑃𝑃18𝑉𝑉 = (18) ∗ 𝐼𝐼𝑣𝑣 = 18𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 18𝐼𝐼𝑣𝑣 𝑊𝑊 𝑃𝑃12𝑉𝑉 = (−12) ∗ 𝐼𝐼𝑣𝑣 = −12𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 12𝐼𝐼𝑣𝑣 𝑊𝑊 𝑃𝑃6𝑉𝑉 = (6) ∗ 𝐼𝐼𝑣𝑣 = 6𝐼𝐼𝑣𝑣 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 6𝐼𝐼𝑣𝑣 𝑊𝑊 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑃𝑃𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑎𝑎 48 + 24 + 12𝐼𝐼𝑣𝑣 = 8 + 16 + 18𝐼𝐼𝑣𝑣 + 6𝐼𝐼𝑣𝑣 𝐼𝐼𝑣𝑣 = 4𝐴𝐴 𝑃𝑃10𝑉𝑉 = (10) ∗ 3 = 30 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟑𝟑𝟒𝟒 𝑾𝑾 𝑃𝑃6𝑉𝑉 = (6) ∗ 3 = 18 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟏𝟏𝟖𝟖 𝑾𝑾 𝑃𝑃9𝐴𝐴 = (−16) ∗ 9 = −144 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟏𝟏𝟐𝟐𝟐𝟐 𝑾𝑾 𝑃𝑃𝑉𝑉𝑠𝑠 = (𝑉𝑉𝑆𝑆) ∗ 6 = 6𝑉𝑉𝑆𝑆 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 6𝑉𝑉𝑆𝑆 𝑊𝑊 𝑃𝑃8𝑉𝑉 = (8) ∗ 6 = 48 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 48 𝑊𝑊 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑃𝑃𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑎𝑎 144 = 30 + 18 + 6𝑉𝑉𝑆𝑆 + 48 𝑉𝑉𝑆𝑆 = 8 𝑣𝑣 𝑃𝑃𝑉𝑉𝑠𝑠 = (8) ∗ 6 = 48 𝑊𝑊 → 𝐴𝐴𝐴𝐴𝑆𝑆𝐴𝐴𝑆𝑆𝐴𝐴𝑏𝑏 48 𝑊𝑊 𝑃𝑃24𝑉𝑉 = (−24) ∗ 6 = −144 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟏𝟏𝟐𝟐𝟐𝟐𝑾𝑾 𝑃𝑃4𝐼𝐼𝑣𝑣 = (−4) ∗ (2) ∗ 3 = −24 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟐𝟐𝟐𝟐 𝑾𝑾 𝑃𝑃1 = (8) ∗ (6) = 48 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟐𝟐𝟖𝟖 𝑾𝑾 𝑃𝑃2 = (10) ∗ 4 = 40𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟐𝟐𝟒𝟒𝑾𝑾 𝑃𝑃3 = (6) ∗ 𝐼𝐼0 = 6𝐼𝐼0 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟔𝟔𝑰𝑰𝟒𝟒 𝑾𝑾 𝑃𝑃4 = (16) ∗ 2 = 32 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟑𝟑𝟐𝟐 𝑾𝑾 𝑃𝑃5 = (6) ∗ 1 = 6 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟔𝟔𝑾𝑾 𝑃𝑃6 = (8) ∗ 3 = 24 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟐𝟐𝟐𝟐 𝑾𝑾 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑃𝑃𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑎𝑎 144 + 24 = 48 + 40 + 6𝐼𝐼0 + 32 + 6 + 24 𝐼𝐼0 = 3𝐴𝐴 𝑃𝑃3𝐼𝐼𝑥𝑥 = (−3) ∗ (2) ∗ 2 = −12 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟏𝟏𝟐𝟐 𝑾𝑾 𝑃𝑃24𝑉𝑉 = (−24) ∗ 4 = −96 𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟗𝟗𝟔𝟔 𝑾𝑾 𝑃𝑃12𝑉𝑉 = (12) ∗ 6 = 72𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟕𝟕𝟐𝟐 𝑾𝑾 𝑃𝑃15𝑉𝑉 = (15) ∗ 4 = 60 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟔𝟔𝟒𝟒 𝑾𝑾 𝑃𝑃1 = (12) ∗ 2 = 24 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟐𝟐𝟐𝟐 𝑾𝑾 𝑃𝑃2 = (−6) ∗ 4 = −24𝑊𝑊 → 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟐𝟐𝟐𝟐𝑾𝑾 𝑃𝑃3 = (6) ∗ 2 = 12 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟏𝟏𝟐𝟐 𝑾𝑾 𝑃𝑃4 = (9) ∗ 4 = 36 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟑𝟑𝟔𝟔 𝑾𝑾 𝑃𝑃5 = (24) ∗ 2 = 48 𝑊𝑊 → 𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒔𝒔𝒂𝒂𝒂𝒂 𝟐𝟐𝟖𝟖 𝑾𝑾 Teorema Tellegem 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − 𝑃𝑃𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑠𝑠𝑎𝑎𝑎𝑎 = 0 (12 + 96 + 60 + 24) − (72 + 24 + 12 + 36 + 48) = 0 192− 192 = 0 Si satisface el teorema de Tellegem