184_projects:austin_snafu_24 [Projects & Practices in Physics]

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===== Project: Lakeview, we have a snafu =====

==== Kick Off Questions ====
  - If capacitors are combined in series does that increase or decrease the total capacitance? What about parallel capacitors?
  - Draw the I vs t, V vs t, and Q vs t graphs for charging & discharging the capacitors.
  - Why is it important to have a current limit in circuits? (What happens to wires if there is a very high current?)


==== Main Problem ====
With your help, the FTOE staff have repaired the damage and are almost ready to restart the hawkion accelerator.  However, they had to cut the lab systems off from Lakeview completely to ensure Manny can't hack in again and do more damage.  The onsite backup generators provide enough power for the lab, but when the FTOE staff tried to power up the control systems they discovered that some critical circuit boards got fried during the emergency.  As a result, you need to create a new circuit that will allow you to provide different amounts of energy to various important systems.

The hawkion generator has a total resistance of 65 $\Omega$, and includes an initiator beam and a set of focusing magnets.
The focusing magnets require a short burst of 200 J to power-up.
The initiator beam requires a short burst of 300 J to power-up.

You need to be able to deliver different amounts of power to the hawkion generator; however, you are not sure that the 100 V primary power supply in the particle generator will be sufficient to power these systems. You manage to find some additional batteries (three 10 V batteries from the supply room) to use if you need them. 

You also have several 0.125F capacitors and a variety of resistors (1 $\Omega$, 5 $\Omega$, 10 $\Omega$, 50 $\Omega$, 100 $\Omega$) on hand. 
You also have access to multiple switches that can be used to open and close parts of the circuit you are designing.  

There is a breaker in the circuit that is a failsafe and will trip if the current reaches 2 A. You also know that there are delicate circuit elements in the generator system, so the generator systems should not be connected to any power supplies when you are charging capacitors.

You should provide a circuit diagram of your design to help you explain to Director Lewis that the current in the circuit is safe and that you are going to be able to supply the needed power to the systems when the time comes to start the accelerator. As a check for yourself, you should make sure that the voltage in the circuit adds up to the correct amount as to not suffer any voltage shortages.

<WRAP info>
=== Learning Goals ===
  * Understand how capacitors charge and discharge
  * Use the relationship between capacitance and energy
  * Understand what happens when capacitors are in parallel or in series
  * Understand how capacitors and resistors combine in a complex circuit
  * Design a circuit that can charge/discharge capacitors & meet specifications
</WRAP>

==== Wrap Up Questions ====
  - Where did you place switches in your circuit? What positions do they need to be in to charge & discharge the capacitors? 
  - How did you limit the current to be under 2 A? 
  - What assumptions did you make in this problem? Why did you need to make them?
  - Suppose you have a 9 V battery connected in series to a capacitor and resistor. If the capacitor is initially uncharged, what is the voltage on that capacitor? What is the voltage on the resistor? If the capacitor is fully charge, what is the voltage on the capacitor? What is the voltage on the resistor?
  - If you wanted to increase the capacitance in your circuit, name 3 ways that you could increase the total capacitance.