Exam (elaborations)
Uitwerkingen Oefenopgaves Kirchoff Hofstede VWO
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Uitwerkingen van de oefenopgaves Kirchhoff uit het Hofstede uitleg- en oefenblad
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1. Zie hiernaast. Er zijn 4 knooppunten en 3 lussenDat geeft de vergelijkingen;
K1: I1 - I 3 - I 2 = 0
K2: I3 - I 5 - I 4 = 0
K3: I2 + I 5 - I 6 = 0
K4: I6 + I 4 - I 7 = 0
L1: 2I2 - 2I5 - 2I3 = 0
L2: 2I3 + 2I4 + 10 + 2I1 = 0
L3: 2I5 - 2I4 = 0
De laatste vergelijking geeft I4 = I5, dus kan overal I4 door I5 worden vervangen:
(verder kunnen alle 2-en ook weggedeeld worden)
K1: I1 - I3 - I2 = 0
K2: I3 - I5 - I5 = 0 ⇒ I3 - 2I5 = 0
K3: I2 + I5 - I6 = 0
K4: I6 + I5 - I7 = 0
L1: I2 - I5 - I3 = 0
L2: I3 + I5 + 5 + I1 = 0
L3: I5 = I4
De tweede vergelijking geeft I3 = 2I5, dus kan overal I3 vervangen worden:
K1: I1 - 2I5 - I2 = 0
K2: I3 = 2I5
K3: I2 + I5 - I6 = 0
K4: I6 + I5 - I7 = 0
L1: I2 - I5 - 2I5 = 0 ⇒ I2 - 3I5 = 0
L2: 2I5 + I5 + 5 + I1 = 0 ⇒ 3I5 + 5 + I1 = 0
De vijfde vergelijking geeft I2 = 3I5 dus kan overal I2 vervangen worden:
K1: I1 - 2I5 - 3I5 = 0 ⇒ I1 - 5I5 = 0
K3: 3I5 + I5 - I6 = 0 ⇒ 4I5 - I6 = 0
K4: I6 + I 5 - I 7 = 0
L1: I2 = 3I5
L2: 3I5 + 5 + I1 = 0
De eerste vergelijking geeft I1 = 5I5 dus kan overal I1 vervangen worden:
K1: I1 = 5I5
K3: 4I5 - I6 = 0
K4: I6 + I5 - I7 = 0
L2: 3I5 + 5 + 5I5 = 0 ⇒ 8I5 + 5 = 0
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