S). Table A.1 compares common AWG values with copper wire diameter in millimeters and the resistance in ohms per kilometer (S2/km). A.4 RESISTANCES IN SERIES AND IN PARALLEL, AND KIRCHHOFF'S LAWS As previously discussed, the total resistance of series resistors is equal to the sum of the individual resistances. If we refer to Figure A.3, the total resistance, RT is RT=R1+R2+R3. (A.4) Resistances in parallel are another matter. Consider Figure A.5. Here the current in the circuit divides and each resistor carries its share. Now apply Ohm's law and we find that the current across each resistor must be equal to the potential measured across the particular resistor divided by its value in ohms. In this particular circuit (Figure A.5), the potential across either resistor is equal to the emf supplied by the battery. In reality the battery is supplying two currents, one through resistor W-X and the second through y-z. For any circuit having two resistors in parallel, the current supplied to the combination must be greater than the current supplied to either branch. It follows, then, that we could replace these two resistors with a single resistor in series with the emf supply, and the value of that resistor must be less than the ohmic value of either single resistor in parallel. A.4.1 Kirchhoff's First Law The first law states that at any point in an electrical circuit there is as much current flowing to the point as away from it. The laws applies no matter how many branches Figure A.5 Model of a circuit with two resistances in parallel and a battery as the emf source. A.4 RESISTANCES IN SERIES AND IN PARALLEL, AND KIRCHHOFF'S LAWS there are in the circuit. Figure A.5 shows point K in the circuit. Let I be the current being supplied by the battery emf source to the combination of the two resistors in parallel; I 1 and I2 are the currents through the two resistors, respectively. We now can say, based on Kirchhoff's first law, that I=I+I. (A.5) Again consider the circuit in Figure A.5. Let R be the equivalent resistance 