 ## By Pavel Panchekha & Jeffrey Prouty

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# Delve AP Physics C Quiz 6

The copy of the test used in class is available, with the multiple choice and free response sections separate.

## Multiple Choice

1. A circuit consists of a capacitor, a battery, and a resistor in series. As a dielectric is slowly inserted into the capacitor:
1. The voltage across the capacitor increases
2. The voltage across the capacitor decreases
3. The charge on each plate of the capacitor increases
4. The charge on each plate of the capacitor decreases
5. Neither the voltage nor charge changes
2. Which of the following parallel-plate capacitors has highest capacitance?
1. Plates of area $$A$$, separated by distance $$d$$, and filled with dielectric of constant $$k$$.
2. Plates of area $$2A$$, separated by distance $$3d$$, and filled with dielectric of constant $$\frac43 k$$.
3. Plates of area $$A/2$$, separated by distance $$d/2$$, and filled with dielectric of constant $$5k$$.
4. Plates of area $$3A$$, separated by distance $$d/4$$, and filled with dielectric of constant $$k/10$$.
5. Plates of area $$\frac32 A$$, separated by distance $$3 d$$, and filled with dielectric of constant $$2 k$$.
3. A circuit contains a $$10 V$$ battery, a $$3 \Omega$$ resistor, and a $$1 \mu F$$ capacitor; how much energy is eventually stored in the capacitor?
1. $$10 \mu J$$
2. $$25 \mu J$$
3. $$50 \mu J$$
4. $$100 \mu J$$
5. $$250 \mu J$$
4. What is the time constant $$\tau$$ of the capacitor from Problem 3?
1. $$1 \mu s$$
2. $$3 \mu s$$
3. $$10 \mu s$$
4. $$30 \mu s$$
5. $$100 \mu s$$
5. How much energy is stored in the capacitor from Problem 3 after $$\tau$$ time has passed?
1. $$4.0 \mu J$$
2. $$6.3 \mu J$$
3. $$15.8 \mu J$$
4. $$19.8 \mu J$$
5. $$31.5 \mu J$$
6. An inductor contains a uniform magnetic field of $$0.4 mT$$. What is the energy density inside the inductor?
1. $$2.51 \cdot 10^{-10} \cdot J m^{-3}$$
2. $$0.064 \cdot J m^{-3}$$
3. $$0.127 \cdot J m^{-3}$$
4. $$159 \cdot J m^{-3}$$
5. $$318 \cdot J m^{-3}$$
7. Which of the following must make a capacitor discharge slower?
1. Decreasing resistance and decreasing capacitance
2. Increasing resistance and decreasing capacitance
3. Decreasing resistance and increasing capacitance
4. Increasing resistance and increasing capacitance
5. None of the above
8. You have four $$1 \mu F$$ capacitors, which you can arrange in a circuit. Which of the following effective capacitances can this circuit not have?
1. $$4 \mu F$$
2. $$\frac52 \mu F$$
3. $$\frac43 \mu F$$
4. $$1 \mu F$$
5. $$\frac12 \mu F$$
9. A inductor is made of a large solenoid with length $$l$$ and $$n$$ turns. Which of the following changes must decrease the inductance $$L$$ of the inductor?
1. Decreasing the length and decreasing the number of turns
2. Decreasing the length and increasing the number of turns
3. Increasing the length and decreasing the number of turns
4. Increasing the length and increasing the number of turns
5. None of these changes are guaranteed to decrease the inductance
10. Which of the following series circuits has the most current flowing through it after $$1 s$$, if a $$1 V$$ battery is attached?
1. $$1 \Omega$$ resistor, $$1 F$$ capacitor
2. $$2 \Omega$$ resistor, $$\frac13 F$$ capacitor
3. $$1 \Omega$$ resistor, $$1 h$$ inductor
4. $$2 \Omega$$ resistor, $$\frac13 h$$ inductor
5. $$2 \Omega$$ resistor
11. A $$1 h$$, $$3 h$$, and $$5 h$$ inductor are placed in parallel. What is their effective resistance?
1. $$0.50 h$$
2. $$0.65 h$$
3. $$1.0 h$$
4. $$4.0 h$$
5. $$9.0 h$$
12. A $$1 h$$, $$3 h$$, and $$5 h$$ inductor are placed in series. What is their effective resistance?
1. $$0.50 h$$
2. $$0.65 h$$
3. $$1.0 h$$
4. $$4.0 h$$
5. $$9.0 h$$
13. When placed in series, two inductors combine to produce a greater effective inductance. Why is this?
1. The new inductor has greater length
2. The new inductor has greater cross-sectional area
3. The new inductor has lesser length
4. The new inductor has lesser cross-sectional area
5. Two inductors in series actually produce lesser effective inductance
14. When placed in parallel, two capacitors combine to produce a greater effective capacitance. Why is this?
1. The new capacitance has greater separation
2. The new capacitance has greater cross-sectional area
3. The new capacitance has lesser separation
4. The new capacitance has lesser cross-sectional area
5. Two capacitors in parallel actually produce lesser effective capacitance
15. Compare the eventual behavior of the capacitor and inductor in an RC or RL circuit:
1. The capacitor eventually behaves like a large resistor, and so does the inductor
2. The capacitor eventually behaves like a large resistor, the inductor like a wire.
3. The capacitor eventually behaves like a wire, the inductor like a large resistor
4. The capacitor eventually behaves like a wire, and so does the inductor
5. The capacitor and inductor do not reach a steady state, instead oscillating in effective resistance
16. As time passes, the effective resistance of a capacitor increases:
1. Inverse-squared
2. Inversely
3. Linearly
5. Exponentially
17. If an inductor and charged capacitor are linked in a loop, the current in the loop will:
1. Increase linearly with time
2. Decrease linearly with time
3. Decrease inversely with time
4. Increase exponentially with time
5. Oscillate
18. Two inductors are placed very close to one another in parallel. The resulting inductance is a bit larger than what one would expect. Why?
1. The charges moving in the wire are attracted to one another
2. The magnetic fields interfere
3. The mutual inductance of the two wires must be factored in
4. The inductors deform slightly due to the presence of another inductor
5. There is no reason for this; the result must be measurement error
19. Which of the following is a not use for inductors?
1. Reduce surges in a circuit
2. Store energy for later release
3. Transfer current between unconnected circuits
4. Generate heat in heating elements
5. Filter some frequencies from a signal
20. When an RL circuit is switched on, the current flow is initially zero, but slowly increases. Which of the following do not affect the percentage of the final current that is flowing after $$1s$$?
1. The voltage
2. The inductance
3. The resistance
4. The ratio of inductance to resistance
5. The product of inductance and resistance
21. Which of these describe how a capacitor acts?
1. A capacitor starts off allowing current flow, and as it charges it allows increased current flow
2. A capacitor starts off preventing current flow, but as it charges it allows increased current flow
3. A capacitor starts off allowing current flow, but as it charges it decreases current flow
4. A capacitor starts off preventing current flow, and as it charges it continues doing so
5. None of the above
22. How much power does a $$1 h$$ inductor store when connected to a $$3V$$ battery and a $$1 \Omega$$ resistor?
1. $$1 J$$
2. $$1.5 J$$
3. $$3 J$$
4. $$4.5 J$$
5. $$9 J$$
23. An ideal inductor is one which:
1. Has maximal resistance
2. Has maximal inductance
3. Has maximal capacitance
4. Has maximal ratio of resistance to inductance
5. Has minimal resistance and capacitance
24. If the time constant of an RC circuit is $$1 s$$, how many seconds must pass before the capacitor is $\frac23$-charged?
1. $$0.33 s$$
2. $$0.41 s$$
3. $$0.67 s$$
4. $$1.1 s$$
5. $$1.5 s$$
25. Where is the energy of an inductor stored?
1. In the charges flowing through its wires
2. In its geometric shape
3. In the current flowing though it
4. In the heat it generates
5. In the field inside it

## Solutions

### Multiple Choice

 1-10 D D C D D B D E A D 11-20 B E A B B E E C D A 21-25 E D E D E