the clockwise direction as positive, and the counterclockwise as negative. For instance, all emfs are labeled positive that tend to make the current flow in the positive direction; and all potential drops are labeled negative, due to this flow of current as well as any emfs tending to make current flow in the opposite direction. When carrying out this exercise, we may find a solution to an equation may be preceded by a minus sign. This merely means that the actual direction of flow of current is opposite to the direction we assumed. Example Calculation of a Series-Parallel Circuit. Figure A.8 is a model series-parallel circuit. In other words, the circuit has a mix of resistances in series and in parallel. Hint: Replace all parallel resistors by their equivalent value first. Thus we end up with a circuit entirely of resistances in series. In other words, first calculate the equivalent resistance for resistors R1 and R2; then for R3, R4, and R5. We end up with four resistors in series: the first and second group of parallel resistors, the R6, and R7. The total resistance of the circuit is then the sum of these four resistances. Assign the following values to these resistances: R1 = 800 S2; R2 = 1200 S2; R3 = 3000 S2; R4 = 5000 S2; R5 = 4000 S2; R6 = 600 S2; and R7 = 900 $ S. REVIEW OF FUNDAMENTALS OF ELECTRICITY WITH TELECOMMUNICATION APPLICATIONS Figure A.8 A model for a circuit with series and parallel resistances with a battery as an emf source. For the first group of parallel resistances we use formula (A.9): R = 800 X 1200/(800 + 1200) = 960,000/2000 = 480 $ S. For the second group of parallel resistances use formulas (A.10) and (A.11), as follows: Calculate the current flowing out of the 48-V battery? G3 = 1/3000 = 0.000333; G4 = 1/5000 = 0.0002; G5 = 1/4000 = 0.00025. Sum these values using Eq. (A.11) and G = 0.000333 + 0.0002 + 0.00025 = 0.000783. Use formula (A.10) to obtain the equivalent resistance R = =1/G = 1/0.000783 = 1277.14 S. Calculate the total resistance of the circuit with the four resistances