With reference to Example 18.10, determine the best combination of current magnitude and wire diameter to reduce the volume of the solenoid coil to a minimum. Will this minimum volume result in the lowest possible resistance? How does the power dissipation of the coil change with the wire gauge and current value? To solve this problem, you will need to find a table of wire gauge diameter, resistance, and current ratings. Table 2.2 in this book contains some information. The solution can only be found numerically.

Question

Example 18.10



Figure 18.40 depicts a simplified representation of a solenoid. The restoring force for the plunger is provided by a spring.

1. Derive a general expression for the force exerted on the plunger as a function of the plunger position x.

2. Determine the mmf required to pull the plunger to its end position (x = a).





Assumptions:

Use of Copper wire in solenoid

In order to access the effects of the wire diameter and current magnitude to the volume, resistance, and power dissipated, mathematical expressions need to be developed for each variable.

Answer 1

Analysis:



Using a chart for AWG wire gauge and current carrying capacity, a table can be developed relating the wire gauge and current carrying capacity to the volume, resistance, and power dissipated.



As the wire gauge increases, the wire diameter and current carrying capacity both decrease and thus the number of turns required increases, and the coil volume decreases. However, the resistance also increases with an increase in wire gauge. Hence, the minimum volume will not result in the lowest possible resistance. Finally, the power dissipation decreases with the increase of wire gauge due to decrease in current capacity.