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Resistors in series and parallel Series Equivalent Resistance Parallel n Req = R1 + R2 + R3 + ... = ∑ Ri i =1 n 1 1 1 1 1 = + + + ... = ∑ Req R1 R2 R3 i =1 Ri 2 EF 152 Fall, 2009 Lecture 4-7 Kirchhoff’s rules EF 152 Fall, 2009 Lecture 4-7 Kirchhoff’s rules step-by-step Loop Rule Junction Rule ∑V = 0 ∑I = 0 1. 2. 3. 4. 5. 6. 7. 8. 9. Sign convention for junctions: Use + for in, - for out I1+I2-I3=0, I3=I1+I2 EF 152 Fall, 2009 Lecture 4-7 3 4 Draw a large diagram Label all quantities (V, R, I for each path), assume a direction for unknown I’s Identify unknown values Use junction rule to reduce number of unknown currents. Use all but one junction. Use + for in, - for out. Choose a closed loop and assume a direction of travel Apply ΣV=0 for the loop, be careful with signs Repeat ΣV=0 for other loops until you have enough equations. Be sure to chose loops so all paths are included at least once. Solve simultaneous linear equations. If you get a negative answer it means the direction is opposite the assumption. EF 152 Fall, 2009 Lecture 4-7 5 Example Solutions – Excel, Matlab, TI-83 Find the current in each part of the circuit and the equivalent resistance of the network. Microsoft Office Excel 2007 Workbook 6 EF 152 Fall, 2009 Lecture 4-7 R-C circuits τ = RC ________________ or __________________ Lower-case i, q, v mean ___________________ Charging q = CE (1 − e − t /( RC ) ) = Q f (1 − e −t /( RC ) ) Discharging q = Q0e −t /( RC ) Capacitor dq E −t /( RC ) Capacitor dq − Q0 −t /( RC ) dt = EF 152 Fall, 2009 Lecture 4-7 R e 7 Applications R-C stands for _____________________ i= EF 152 Fall, 2009 Lecture 4-7 = I 0e i= dt = RC e −t /( RC ) = I 0 e −t /( RC ) 8 EF 152 Fall, 2009 Lecture 4-7 9