AP Physics Assignment

AP Physics Assignment – Inductance

Reading College Physics – pp. 509 – 521, Chapter 20

University Physics – Chapters 30, 31, 32, 33

Objectives/HW

	The student will be able to:	HW:
1	Define and calculate inductance and solve related problems including those that involve parallel or series inductors.	1 – 8
2	Analyze RL circuits in terms of the appropriate differential equation and resulting exponential functions for charge, current, voltage, etc.	9 – 15
3	Analyze LC and RLC circuits in terms of the appropriate differential equation and resulting exponential functions for charge, current, voltage, etc.	16 – 18

Homework Problems

1. An inductor is any coil or loop of wire and may be described as a “moderator” of current. Explain this by answering the following questions: (a) If there is a current through the loop, why must there be magnetic flux through the same loop? (b) If the current increases, why must the magnetic flux also increase? (c) According to Lenz’s Law an emf is induced in what direction or sense relative to the current? (d) Why would this have a moderating effect? (e) What happens if the current decreases?

2. (a) If can be said that any and every electrical circuit has a certain amount of inductance – explain. (b) Having said that, unless there is a multiple-turn coil in the circuit the amount of inductance will be negligible – explain.

3. An inductor of 12 mH of negligible resistance is arranged vertically and the current through it is controlled by a variable power supply. Taking a positive value to mean that the top of the inductor is “positive”, find the emf in each of the following cases: (a) Current is 2.0 A upward and constant. (b) Current is 2.0 A upward and decreasing at 5.0 A/s. (c) Current is 5.0 A downward and increasing at 2.0 A/s. (d) Current is 0.100 A downward and decreasing at 2.0 A/s.

4. A certain inductor consists of a coil of wire that has a resistance of 5.0 W and an inductance of 2.0 mH. A current of 20.0 mA passes to the right through the inductor. Find the potential difference of the right side of the inductor relative to the left side should one of the following occur: (a) The current remains constant. (b) The current increases at 20.0 A/s. (c) The current decreases at 5.0 A/s.

5. A student uses a computer to measure the current and emf for a coil of wire of negligible resistance. It is found that the emf of the coil is 35 mV as the current increases from 155 mA to 195 mA in 0.0100 seconds. What is the inductance of the coil?

6. Show that inductance may be defined as magnetic flux per current by setting the emf of an inductor equal to Faraday’s Law and solving for the inductance.

7. An inductor is made by wrapping wire around a wooden dowel of length 15.0 cm and diameter 2.00 cm. If wrapped as tightly as possible, the wire forms 45 turns per centimeter. (a) Determine the inductance if one layer of wire is wrapped tightly from end to end. (b) In order to achieve a higher inductance, multiple layers of wire can be wrapped. How many total turns would be required to achieve 5.0 mH?

8. A certain square coil of wire consists of 100 turns and has an inductance of 2.0 mH. Find the inductance of (a) a square coil with the same number of turns but twice the area, (b) a coil with the same area but with 200 turns.

9. The current through a 0.30 mH inductor varies according to I = 2 cos(380t), where I is in amperes and t is in seconds. (a) Find the emf of the inductor at t = 0.10 s. (b) What is the maximum emf? (c) All other parameters being the same, what angular frequency of the current would be required to yield a maximum emf of 0.50 volt?

10. In the circuit shown below the switch is closed at t = 0 and then reopened at t = 10.0 s. (a) Find the voltage and current of the inductor at t = 0. (b) Find the voltage and current of the inductor at t = 10.0 s. (c) Sketch graphs of voltage vs. time and current vs. time for the inductor. (d) If the inductor is 10.0 mH, what is the rate of change in its current at t = 0 and at t = 10.0 s? (e) Which of your answers, if any, would change with a different inductor?

11. Examine the circuit shown below in which the switch has been in the closed position. (a) Find the current and voltage of the inductor immediately after the switch is opened. The switch remains open for a long time. (b) Find the current and voltage of the inductor immediately after the switch is closed again.

12. The switch in the circuit shown below is closed at t = 0 and then reopened at t = 10.0 s. (a) Find the voltage across each inductor at t = 0. (b) Find the rate of change in the voltage across R₂ at t = 0. (c) Find the voltage across each inductor at t = 10.0 s. (d) Find the rate of change in the voltage across R₂ at t = 10.0 s. (e) Produce a detailed sketch of the graph voltage vs. time for the inductor L₁.

13. A slinky with 175 turns, radius 3.50 cm, and resistance 8.0 W is stretched to a length of 90.0 cm. A battery with emf 5.70 V and internal resistance 2.0 W is connected to establish a current through the slinky. (a) What will be the maximum current through the slinky if it stays connected to the battery? (b) How much time will it take for the current to go from zero to 90.0% of its maximum? (c) What is the emf of the slinky and what is the voltage across it at that same point in time?

14. An inductor of 75 mH and negligible resistance is “discharging” through a resistor of 550 W (the two devices are connected in a simple series loop). The current at t = 0 is 20.0 mA. (a) Find the initial voltage across the inductor. (b) Find the initial rate of change in the current. (c) Find the current and voltage at t = 0.100 ms. (d) Find the total heat dissipated by the resistor as the current drops to zero. (e) A capacitor of what capacitance and what initial charge would discharge identically if connected to the same resistor?

15. In the circuit shown below the emf = 12.0 V, L = 44 mH, and R = 50.0 W. (a) Find the change in the steady state current through the battery when the switch is moved from open to closed. (b) How much time does it take for 99.0% of this change to occur? (c) How much time does it take for 99.0% of the change to occur when the switch is reopened? (d) Make a careful sketch of the voltage vs. time graph for the inductor, including appropriate numerical values.

16. A capacitor of 2200 μF is charged to 6.0 V by a battery. Then it is removed from the battery and at t = 0 it is connected to an inductor of 11 mH. Ignore resistance. (a) With what frequency will the voltage of the capacitor oscillate? (b) What is the maximum current and at what value of t does it first occur? (c) How much energy is in the system? (d) At what voltage and current is the energy equally split between that of the capacitor and that of the inductor?

17. A certain Tesla coil has a solenoid of diameter 8.0 cm, length 30.0 cm, and 660 turns of wire. Attached to one end of the wire atop the solenoid is a metal sphere of diameter 20.0 cm. The other end of the wire leads to ground (earth). This forms in essence an LC circuit in which the L is the solenoid and the C is the isolated sphere (in conjunction with the Earth which can be taken as “infinity”). When in operation, a high frequency current passes back and forth through the solenoid as the sphere takes on charge of opposite sign at the same frequency. Ignore resistance. (a) Find the frequency of the oscillations in current and charge. (b) If the maximum voltage of the sphere is 110 kV, how much energy is present? (c) What is the maximum current? (d) A separate LC circuit with the same frequency is used to “excite” the solenoid and sphere. If this circuit has an inductor of 12 μH, what must be the value of the capacitor?

18. In an oscillating LC circuit, the maximum charge on the capacitor is 2.0 μC and the maximum current through the inductor is 6.0 mA. (a) Determine the frequency of the oscillations. (b) If the maximum voltage is 0.30 V, what are the values of L and C?