PHY132_L11

PHY132_L11 - Classical Physics II Classical Physics II...

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lassical Physics II Classical Physics II PHY132 Lecture 11 Circuits II Lecture 11 1 02/19/2010

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Kirchhoff’s Rule #1 Based on conservation of charge (carriers): “in any circuit NODE, the sum of all currents must be zero”, i.e. no net charge is created or destroyed per unit time… – we define in-going currents as +ve and outgoing currents as –ve: = 0 irchhoff’s Rule #1) I 1 + I 2 I 3 I 4 0 (Kirchhoff s Rule #1) I 5 I 4 –Note : after so lv ing the set of equations and finding I , I , I , etc., we I 1 I 2 1 2 3 may discover that one or more are negative; again, • that just means that the correct direction of the (+ve) charge flow I i is opposite to the original guess! 02/19/2010 Lecture 11 2
Example Consider the circuit below: – Note the ~ arbitrary choice of current directions ; if I got them rong, I’ll notice from – e igns I 1 0 V wrong, I ll notice from ve signs!) – Net sum of currents in node A ; all currents in , thus: I 1 + I 2 + I = 0 …(1) e have: 0 e ame! I 2 2   10 V b 20 V 1 3 4 a in B we have: I 1 I 2 I = 0 i.e. same! Kirchhoff’s Rule #2 (voltage): a A c a : +10 – 2 I 1 +10 I –3 I 1 = 0 …(2) I   10 B A c b A c b : +20 – I 2 + 10 I –4 I 2 = 0 …(3) 3 eq’ns, 3 unknown currents solve: (2) & (1): 10–5 I –10( I + I ) = 10–15 I –10 I = 0 1 1 2 1 2 I 2 =1 – 1.5 I 1 …(4) (3) & (1): 20–5 I 2 –10( I 1 + I 2 ) = 20 15 I 2 –10 I 1

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PHY132_L11 - Classical Physics II Classical Physics II...

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