I3 whatisi2 whichofthefollowingequationsisnotcorrect a

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Unformatted text preview: ircuit, assume Vi and Ri are known. What is I2 ?? • How many equations do we need to write down in order to solve for I2? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 • Why?? – – We have 3 unknowns: I1, I2, and I3 We need 3 independent equations to solve for these unknowns (3) Choose loops and directions Physics 212 Lecture 10, Slide 16 Physics 212 Lecture 10, Slide V1 R1 ++ - V2 R2 -+ + R3 - - ++ - V3 - I1 I2 Calculation In this circuit, assume Vi and Ri are known. I3 What is I2 ?? • Which of the following equations is NOT correct? (A) I2 = I1 + I3 (B) ­ V1 + I1R1 ­ I3R3 + V3 = 0 (C) ­ V3 + I3R3 + I2R2 + V2 = 0 (D) ­ V2 – I2R2 + I1R1 + V1 = 0 • Why?? – – (4) Write down voltage drops (5) Write down node equation (D) is an attempt to write down KVR for the top loop Start at negative terminal of V2 and go clockwise • Vgain (­V2) then Vgain (­I2R2) then Vgain (­I1R1) then Vdrop (+V1) Physics 212 Lecture 10, Slide 17 Physics 212 Lecture 10, Slide R1 V1 R2 V2 R3 V3 I1 Calculation I2 I3 • We have the following 4 equations: 1. I2 = I1 + I3 2. ­ V1 + I1R1 ­ I3R3 + V3 = 0 3. ­ V3 + I3R3 + I2R2 + V2 = 0 4. ­ V2 – I2R2 ­ I1R1 + V1 = 0 • Why?? – – – In this circuit, assume Vi and Ri are known. 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 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 18 Physics 212 Lecture 10, Slide R1 V1 R2 V2 R3 R 2R R V3 2V V V I1 Calculation In this circuit, assume Vi and Ri are known. I2 What is I2 ?? I3 • We have 3 equations and 3 unknowns. I1 (6) Solve the equations I2 I3 I2 = I1 + I3 V1 + I1R1 ­ I3R3 + V3 = 0 V2 – I2R2 ­ I1R1 + V1 = 0 •The solution will get very messy! Simplify: assume V2 = V3 = V V1 = 2V R1 = R3 = R R2 = 2R Physics 212 Lecture 10, Slide 19 Physics 212 Lect...
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