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Electric Circuits, 9th Edition P33. Designed for use in a one or two-semester Introductory Circuit Analysis or Circuit Theory Course taught in Electrical or Computer Engineering Departments. Electric Circuits 9/e is the most widely used introductory circuits textbook of the past 25 years. As this book has evolved over the years to meet the changing learning styles of students, importantly, the underlying teaching approaches and philosophies remain unchanged. | 296 Natural and Step Responses of RLC Circuits To find the maximum value of Sp we find the smallest positive value of time where dv dt is zero and then evaluate vsp at this instant. The expression for imax is t _ 1 x -1 max tan I o d a 8.99 See Problem 8.67 For the component values in the problem statement we have R 4 x 103 a - 666.67 rad s lLj o and V V2 666-67 2 28 859-81 rad s. Substituting these values into Eq. 8.99 gives 6nax 53.63 IS. Now use Eq. 8.98 to find the maximum spark plug voltage fspGmax Mfmax -25 975.69 V. b The voltage across the capacitor at rmax is obtained from Eq. 8.97 as tmax 262.15 V. The dielectric strength of air is approximately 3 x 106 V m so this result tells us that the switch contacts must be separated by 262.15 3 x 106 or 87.38 cm to prevent arcing at the points at imax. In the design and testing of ignition systems consideration must be given to nonuniform fuel-air mixtures the widening of the spark plug gap over time due to the erosion of the plug electrodes the relationship between available spark plug voltage and engine speed the time it takes the primary current to build up to its initial value after the switch is closed and the amount of maintenance required to ensure reliable operation. We can use the preceding analysis of a conventional ignition system to explain why electronic switching has replaced mechanical switching in today s automobiles. First the current emphasis on fuel economy and exhaust emissions requires a spark plug with a wider gap. This in turn requires a higher available spark plug voltage. These higher voltages up to 40 kV cannot be achieved with mechanical switching. Electronic switching also permits higher initial currents in the primary winding of the autotransformer. This means the initial stored energy in the system is larger and hence a wider range of fuel-air mixtures and running conditions can be accommodated. Finally the electronic switching circuit eliminates the need for the point contacts. This .