# I3 we have the following 4 equations 1 2 2 3 3 4 i2

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Unformatted text preview: 4 equations: 1. 2. 2. 3. 3. 4. I2 = I1 + I3 - V1 + I1R1 - I3R3 + V3 = 0 - V3 + I3R3 + I2R2 + V2 = 0 - V2 – I2R2 - I1R1 + V1 = 0 What is I2 ?? We need 3 equations: Which 3 should we use? A) Any 3 will do B) 1, 2, and 4 C) 2, 3, and 4 • Why?? – – – We need 3 INDEPENDENT equations Equations 2, 3, and 4 are NOT INDEPENDENT • Eqn 2 + Eqn 3 = - Eqn 4 We must choose Equation 1 and any two of the remaining ( 2, 3, and 4) Physics 212 Lecture 10, Slide 14 14 R1 R2 R3 V1 V2 V3 I1 I2 I3 Calculation In this circuit, assume Vi and Ri are known. What is I2 ?? • We have 3 equations and 3 unknowns. I2 = I1 + I3 V1 + I1R1 - I3R3 + V3 = 0 V2 – I2R2 - I1R1 + V1 = 0 R 2R R 2V V V I1 •The solution will get very messy! I2 I3 Simplify: assume V2 = V3 = V V1 = 2V R1 = R3 = R R2 = 2R Physics 212 Lecture 10, Slide 15 15 Calculation: Simplify In this circuit, assume V and R are known. R 2R R 2V V V I1 I2 What is I2 ?? • We have 3 equations and 3 unknowns. I2 = I1 + I3 -2V + I1R - I3R + V = 0 (outside) -V – I2(2R) - I1R + 2V= 0 (top) I3 current current direction direction • With this simplification, you can verify: I2 = ( 1/5) V/R I1 = ( 3/5) V/R I3 = (-2/5) V/R Physics 212 Lecture 10, Slide 16 16 Follow-Up 2V R I1 • We know: V 2R a • I2 = ( 1/5) V/R I1 = ( 3/5) V/R I3 = (-2/5) V/R I2 b R V BB I3 Suppose we short R3: (A) Vab remains the same remains (B) Vab changes sign (B) changes (C) Vab increases (C) (D) Vab goes to zero What happens to Vab (voltage across R2?) R Why? Redraw: Bottom Loo...
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