184_projects:level_up_c [Projects & Practices in Physics]

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===== Project: NASA Consult Test Part 2 =====
You've impressed Lieutenant Maverick Mitchell with your consulting work over the Artemis 13 disaster. Even though it's been quick, Maverick wants to promote you to Senior Consultants, but just got word that NASA director Dr. Sinnay Tobb still requires some extra vetting. Dr. Tobb has passed along the following tasks to test your mettle, yet again. Complete the levels and show that you're ready to be senior consultants! 

=== Level 1: Basic Combos ===
For the circuits below, say that $V_{bat} = 5 V$, $C_1 = 6 \mu F$, $C_2 = 7 \mu F$, and $C_3 = 8 \mu F$. For each circuit below,

a) What is the equivalent capacitance of the circuit?

b) Which capacitor would have the largest voltage drop?

c) Which capacitor would have the smallest charge?


{{  184_notes:level1circuits_c.png?400  }}


=== Level 2: Equal circuit elements ===
For the circuits below, say that $V_{bat} = 16 V$ and each capacitor is $C = 470 \mu F$. For each circuit,

a) Which capacitors are in series? Which capacitors are in parallel? How do you know?

b) What is the equivalent capacitance of the circuit?



{{  184_notes:level2circuits_c.png?600  }}


=== Level 3: Capacitor Circuits ===
For the circuits below, you have been given some of the quantities for various elements around the circuit. For example, $V_1$ would correspond to the voltage across Capacitor 1. For each circuit,

a) Which capacitors are in series and which capacitors are in parallel? How do you know?

b) Find all the missing quantities for each capacitor (C, V, Q, and U).

c) What is the voltage provided by the battery in your circuit?

d) What is the total charge stored by the circuit? What is the total energy?


{{  184_notes:level3circuits_c.png?600  }}


=== Level 4: Challenge Mode ===
Consider the circuit below where initially the capacitors are all uncharged.

a) Initially (the moment that the switch is closed), where is there current in the circuit?

b) When the switch is closed, what is the initial current provided by the battery if $V_{bat} = 6V$, all resistors are $R = 1000 \Omega$, and all capacitors are $C = 2200 mF$?

c) What would the V vs t, Q vs t, and I vs t graphs look like for each of the capacitors?

d) After the switch has been closed for a long time, where is there current in the circuit?

e) What is the final current provided by the battery? (After the switch has been closed for a long time.)

f) When the switch has been closed for a long time, what is the voltage across each of the capacitors?

g) If the switch is then opened again, what would you expect to happen? Explain in words.

{{  184_notes:level4circuit_c.png?300  }}

<WRAP info>
=== Learning Goals: ===
  * Explain how you know something is in series. Explain what happens for charge & voltage when capacitors are in series.
  * Explain how you know something is in parallel. Explain what happens for charge & voltage when capacitors are in parallel.
  * Explain what the loop rule is and the physical principle it is related to.
  * Explain what the node rule is and the physical principle it is related to.
  * Apply $C = Q/V$ & $ U = 1/2C V^2$ to solve for any unknown quantities in the circuit (U, Q, V, & C).
  * Calculate the total combined capacitance for a given circuit.
</WRAP> 

Conceptual Questions:
  - What are the circuit rules that you used to solve these circuits? When did you use each of them?
  - How do you know if capacitors are in series or parallel (or neither)? What happens to current & voltage in each of those cases?
  - What are the loop & node rules? What physical principles do they relate to?
  - The equation for energy can be written in 3 different ways - what are the 3 ways & how do you get them?
  - What assumptions did you make when solving these circuits? (Hint: there are at least 3 big ones.)