So far, we have considered circuits which can be reduced to a single loop circuit and applied Ohm’s law to extract I and/or V in the circuit. 6 V 5 3

LAW & ORDER Gustav Robert Kirchoff Georg Simon Ohm

Statement of Kirchhoff’s Rules Junction Rule The sum of the currents entering any junction must equal the sum of the currents leaving that junction A statement of Conservation of Charge Loop Rule The sum of the potential differences across all the elements around any closed circuit loop must be zero A statement of Conservation of Energy

Kirchoff’s Rules I2 I1 = I2 + I3 I1 I3 (1) Node rule, current law,.. = +

(2) Loop rule, V-law,.. D B R1 C V R2 E A F V A B C D E F A

V – IR1 – IR2 – IR3 = 0 V = I (R1 + R2 + R3) = I Req IR1 IR2 R1 R2 IR3

V = IReq R1 R2 R3 V I I1 I2 I3 4 unknowns Need 4 independent eqs. V/R1 = I1 (3) V – I2R2 = 0 V/R2 = I2 V (1/R1+1/R2+1/R3) = I (4) V – I3R3 = 0 V/R3 = I3 1/Req V = IReq