Physics 72: Chapter 30 Problem Set Name: Lecturer: Mr Carlos Baldo III
Summer 2010 Score: Section: X7-7
Encircle the letter of the correct answer. Solve each problem clearly and completely for full credit. 1.
Current. Solenoid S1 of radius r, length l, and N1 turns carries a current I1. Solenoid S2 also of length l but with N2 turns is wound uniformly around S1. If I1 is halved, what happens to the mutual inductance of S1 and S2? A. Decreases by a factor of ½ B. Increases by a factor of 2 C. Increases by a factor of 4 D. Decreases by a factor of ¼ E. Remains the same
2.
Inductance. Which of the following will not vary the mutual inductance of two coaxial current-carrying circular coils having the same length? A. Inserting a ferromagnetic Elder’s wand inside one coil. B. Doubling the current through one of the coils. C. Tilting one coil 300 relative to the other. D. Pulling out half the length of the inner coil. E. Reshaping the outer coil from circle to heart.
3.
Magnetic flux. When a coil of inductance 2mH has a current of 40A, what is the value of the total magnetic flux through the coil? A. Zero B. 0.8 Wb C. 0.08 Wb D. 0.16 Wb E. 0.016 Wb
4.
Mutual Inductance. Consider two coaxial solenoids S1 and S2. S1 has N turns, radius r, and length l. S2 has 2N turns, radius r and length 2l. What can you conclude about their inductances? A. M1,2 = M2,1; L1 = L2/2 B. M1,2 = M2,1; L1 = L2 C. M1,2 = M2,1; L1 = 2L2 D. M1,2 = M2,1/2; L1 = L2/2 E. M1,2 = 2M2,1; L1 = 2L2
5.
Self-Inductance. At the instance when the current in the inductor is increasing at the rate of 3 A/s, the magnitude of the induced emf is 12 mV. What is the self-inductance of the inductor? A. 0.002 H B. 0.004 H C. 0.04 H D. 0.20 H E. Zero
6.
Steady A. B. C. D. E.
7.
LC Circuit. Consider a capacitor connected is series with an inductor. At the instant that the capacitor is fully charged, what other parameter/s has/have a maximum value? A. stored electric energy B. voltage across the inductor C. voltage across the capacitor D. A and B E. A and C
current. Which of the following statements is/are FALSE for an inductor at steady current? There is no induced emf across the inductor. There is net energy flow in the inductor. The stored electric field energy is maximum. A and B B and C
Physics 72: Chapter 30 Problem Set
Summer 2010
8.
R-L Circuit. An inductor of inductance 5 µH is connected in series to a 2 Ω resistor, an open switch and a 10 V dc power supply. Immediately after closing the switch, the voltage across the inductor is _________. A. Zero B. 1 µV C. 10 µV D. 1 V E. 10 V
9.
R-L Circuit. Based on the figure, what is the current passing through the battery a long time after the switch S is closed? A. 0 A B. 2 A C. 4 A D. 6 A E. 12 A
10. RLC Circuit. Consider an RLC dc circuit consisting of a resistor R = 20 Ω, an inductor L = 1 mH and a fully charged capacitor C = 10 µF connected in series. The plot of the charge through the circuit as a function of time is __________. A. Oscillating B. Oscillating and exponentially decaying C. Oscillating and exponentially growing D. Exponentially decaying E. Exponentially growing 11. Magnetic field energy. A certain inductor stores a 2.4 J maximum magnetic field energy when a 2-A current passes through it. How much magnetic field energy can the inductor store if the current is increased to 4 A? A. 1.2 J B. 2.4 J C. 4.8 J D. 9.6 J E. 0 J 12. Magnetic energy density. Consider a coaxial cable consisting of a small cylinder (with radius R1) and a bigger hollow cylinder (with radius R2) carrying equal currents in opposite directions as shown. What is the magnetic field energy density at point P a distance r from the center? A. Zero B.
C.
1 µo I 2 2 π 2r 2 1 µo I 2 4 π 2r 2
D.
E.
1 µo I 2 8 π 2r 2 1 µo I 2 16 π 2 r 2
13. RL Circuit plot. Shown are decay plots of currents of 2 R-L circuits with identical inductors. If the resistance of the resistor in circuit X is R, what is the value of the resistance of the resistor in circuit Y? Note: All circuits have the same initial current values? A. ¼ R B. ½ R C. R D. 2 R E. 4 R
Physics 72: Chapter 30 Problem Set
Summer 2010
14. Ideal LC Circuit. Which of the following statements is always correct in an ideal L-C circuit? I. The system has a constant total energy II. The charge on the capacitor and the current through an inductor both vary sinusoidally. III. The direction of current in the circuit is the same in every cycle. A. I only B. II only C. I and II only
D. I and III only E. I, II and III
15. Ideal LC Circuit 2. Which of the following statement is TRUE regarding an L-C circuit? A. Current oscillates with exponentially decreasing amplitude in time. B. Total energy is not conserved. C. Charge on the capacitor oscillates sinusoidally in time. D. The transformation from electric field energy to magnetic field energy varies sinusoidally. E. When the current in the inductor is maximum, the magnitude of the charge in the capacitor is also maximum. 16. RLC Circuit plot. The circuit consists of a resistor R = 20 Ω, an inductor L = 1 mH and a fully-charged capacitor C = 10 µF which are connected in series is __________. A. Undamped B. Underdamped C. Critically-damped D. Overdamped E. None of the above 17. RLC Circuit. Consider the R-L-C circuit shown on the right with R =20 Ω, L = 1 mH, C = 10 µF and V = 12 V. Initially, switch SA is kept closed. After the capacitor is fully-charged, SA is open while SB is closed so that current flows through the resistor and the inductor. What is the voltage across the resistor immediately after the SB is closed? A. Zero B. 2 V C. 4 V D. 6 V E. 12 V
18. Energy density. A coil with inductance L carries a current I. Which of the following will affect the total magnetic energy associated with the coil’s magnetic field? I. Reversing the current direction II. Increasing the current III. Shortening the length of the coil A. I only B. III only C. I and III
D. II and III E. I, II and III
19. Mutual Inductance. The mutual inductance between the two coils of a spark plug was determined to be 0.01 H. If the current in one coil drops from 5.0 A to 0.0 A in the span of 1 ms, what is the emf induced in the other coil? A. -500.0 V B. -50.0 V C. –5.0 V D. 5.0 V E. 50.0 V 20. RLC plots. A series L-R-C circuit without a battery has L = 1 H, R = 1 Ω and C = 1 mF. The capacitor is initially charged. Which graph accurately describes the behaviour of the circuit capacitor charge as a function of time?
Physics 72: Chapter 30 Problem Set
Summer 2010
21. Self-Inductance. An inductor has an inductance of 50.0 mH. If 5.0 V was induced in the same inductor in a span of 2.0 s, what was the average rate of change of the current flowing through it within the same time duration? A. 1.0 A/s B. 5.0 A/s C. 10.0 A/s D. 50.0 A/s E. 100 A/s 22. Induction effect. The switch in the circuit shown below is closed and the light bulb glows steadily. The inductor is a simple air-core solenoid. As an iron rod is being inserted into the interior of the solenoid, the brightness of the light bulb ___________. A. increases B. decreases C. remains the same D. the bulb goes out E. Ayy, ambot! 23. Magnetic Energy. A solenoid of length ℓ contains N turns and has a cross sectional area A. When a current i passes through it, the solenoid stores energy equal to U0. Which of the following will double the amount of energy stored in the solenoid? A. cut i in half B. cut ℓ in half C. double i D. double N E. double ℓ For the next three numbers, a capacitor with capacitance C and storing an initial charge Q is connected to a solenoid with an inductance L. The circuit enters electrical oscillation with angular frequency ω = (LC)-1/2. 24. LC Circuits. At what time t is the charge remaining on the capacitor half the initial charge? A. π(LC)1/2/3 B. π(LC)-1/2/3 C. πLC/3 D. π(LC)1/2/2 E. π(LC)-1/2/2 25. LC Circuits. What is the maximum current that passes through the solenoid? A. ωQ/4 B. ωQ/2 C. ωQ D. 3ωQ/2 E. 2ωQ 26. LC Circuits. What is the current through the solenoid when the energy stored in the capacitor and solenoid is equal? A. ωQ/2 B. ωQ/ 2 C. ωQ D. ωQ 3 /2 E.
ωQ/ 3
27. RL Circuits. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the circuit is closed at time t=0, at which time the current is 0. At any later time t the current i is given by: A. (E/R) ( 1 – exp(-Lt/R) ) B. (E/R) exp(-Lt/R) C. (E/R) ( 1 + exp(-Rt/L) ) D. (E/R) exp(-Rt/L) E.
(E/R) ( 1 – exp(-Rt/L) )
The SAND Prince