Sophomore Engineering Curricula	Introduction	Conservation and Accounting Framework	Curriculum Structure: Texas A&M four-course structure	Curriculum Structure: Texas A&M Five-Course Structure
	Curriculum Structure: Rose-Hulman Institute of Technology Sophomore Engineering Curriculum	Example Problems	Student Performance/Faculty Reactions	Conclusions

Example 2: Jumping a Spark

Consider the circuit given in Figure 3 .

Figure 3 A Switched Circuit.

The circuit has one degree of freedom when the switch is closed and the labeled current gives the flow variable. The problem given to students is to explain what happens to the voltage at V_p when the switch opens after having been closed for a long period of time. With a little help, the student’s thinking proceeds as follows. Conservation of energy tells the students that there is energy stored in the coil due to the flow of current.  When the switch opens, and degree of freedom drops to zero and the current drops to zero causing the energy in the coil to leave the coil. Because the energy cannot disappear, it has to go somewhere.  The energy cannot be dissipated by the resistance R_p if the current is zero. The students conclude that the voltage at V_p becomes very negative until a spark jumps across the switch.  The energy dissipated by jumping the gap is large because even though the current in the spark may be small, the voltage drop is large. Since a significant amount of energy is dissipated across the gap, the students realize that the switch may become damaged.

Next the students are asked to design something to prevent the arc from jumping and damaging the switch. Some students who understand about diodes choose to prevent the degree of freedom from dropping by putting in a clamping diode. Others recognize the real need is to provide a storage location for the energy that leaves the coil. In other words, they increase the order of the system to allow for an additional energy storage mechanism. Their design is shown in Figure 4 :

Figure 4 The Protected Switch.

Since a capacitor stores energy, the energy from the inductor enters the capacitor when the current is stopped. This example demonstrates how degree of freedom and order can be used in design.

The previous two examples demonstrate how augmenting the conservation and accounting with degree of freedom and order can help in system analysis and design. These concepts are not essential and need not be taught if the students are not sufficiently advanced. Without them, students should be encouraged to write all conservation equations for every system.

Examples 3 and 4 were taken from the ES205 final at Rose-Hulman Institute of Technology.   They illustrate the types of problems that students at Rose-Hulman can solve at the end of the sophomore ES20x sequence.  The thermocouple problem illustrates that students can tackle multidisciplinary problems using the conservation and accounting framework.  The vibration analysis of the car also illustrates the power of computer algebra systems such as Maple.  Entering students at Rose-Hulman are required to purchase a notebook computer with a software suite.  Although the car problem can be set up manually, the calculations would be difficult to do by hand, but they are ideal for Maple.  This problem is not much different than what students might see in a senior level vibrations course.

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References

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