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Project 7B: NASA Consult Test Part 2
Lieutenant Maverick Mitchell has been impressed with your work over at JPL and has been considering hiring your team as permanent consultants. Maverick was all ready to sign the hiring paperwork, but just got word that NASA director Dr. Sinnay Tobb requires some extra vetting. Dr. Tobb has passed along the following tasks to test your mettle. Complete the levels and show that you're ready to be permanent 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?
Level 2: Equal circuit elements
For the circuits below, say that $V_{bat} = 16 V$ and each resistor is $C = 470 \mu F$. For each circuit,
a) What is the equivalent capacitance of the circuit?
b) Which capacitors are in series? Which capacitors are in parallel? How do you know?
Level 3: Resistor 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?
Level 4: Challenge Mode
Consider the circuit below where initially the capacitors are all uncharged.
a) Initially, 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) If the switch is then opened again, what would you expect to happen? Explain in words.
Learning Goals:
- Explain how you know something is in series. Explain what happens for current & voltage when capacitors are in series.
- Explain how you know something is in parallel. Explain what happens for current & 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.
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.)