PHYS 2212 Module 10 Self Assessment Practice Problems

Module 10 Self Assessment Practice Problems

A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as in the figure. Terminals a and b of winding A may be connected to a battery through a reversing switch. State whether the induced current in the resistor R is from left to right or from right to left in the following circumstances.
(a) The current in winding A is from a to b and is increasing.
(b) The current in winding A is from b to a and is decreasing.
(c) The current in winding A is from b to a and is increasing.
Answer: (a) right to left  (b) right to left  (c) left to right
When a camera uses a flash, a fully charged capacitor discharges through an inductor. In what time must the 0.100-A current through a 2.00-mH inductor be switched on or off to induce a 500-V emf?
Answer: 0.4 µs
A long, cylindrical solenoid with 100 turns per centimeter has a radius of 1.5 cm.
(a) Neglecting end effects, what is the self-inductance per unit length of the solenoid?
(b) If the current through the solenoid changes at the rate 5.0 A/s, what is the emf induced per unit length?
Answer:    (a) 89 mH/m  (b) 0.44 V/m
A long, straight solenoid has 800 turns. When the current in the solenoid is 2.90 A, the average flux through each turn of the solenoid is 3.25 x 10-3 Wb (webers, the unit for flux). What must be the magnitude of the rate of change of the current in order for the self-induced emf to equal 6.20 mV?
Answer: 6.9 mA/s
A coil with a self-inductance of 3.0 H and a resistance of 100 Ω carries a steady current of 2.0 A.
(a) What is the energy stored in the magnetic field of the coil?
(b) What is the energy per second dissipated in the resistance of the coil?
Answer:  (a) 6 J  (b) 400 J/s
An inductor used in a dc power supply has an inductance of 12.0 H and a resistance of 180 Ω. It carries a current of 0.500 A.
(a) What is the energy stored in the magnetic field?
(b) At what rate is thermal energy developed in the inductor?
(c) Does your answer to part (b) mean that the magnetic-field energy is decreasing with time? Explain.
Answer:   (a) 1.5 J  (b) 45 J/s
In a proton accelerator used in elementary particle physics experiments, the trajectories of protons are controlled by bending magnets that produce a magnetic field of 4.80 T. What is the magnetic-field energy in a 10.0-cm3 volume of space where B = 4.80 T?
Answer: 91.7 J
An inductor with an inductance of 2.50 H and a resistance of 8.00 Ω is connected to the terminals of a battery with an emf of 6.00 V and negligible internal resistance. Find
(a) the initial rate of increase of current in the circuit
(b) the rate of increase of current at the instant when the current is 0.500 A
(c) the current 0.250 s after the circuit is closed
(d) the final steady-state current.
Answer:   (a) 2.4 A/s  (b) 0.8 A/s  (c) 0.41 A  (d) 0.75 A
A 7.50-nF capacitor is charged up to 12.0 V, then disconnected from the power supply and connected in series through a coil. The period of oscillation of the circuit is then measured to be 8.60 x 10-5 s. Calculate:
(a) the inductance of the coil
(b) the maximum charge on the capacitor
(c) the total energy of the circuit
(d) the maximum current in the circuit.
Answer:  (a) 25 mH  (b) 90 nC  (c) 540 nJ  (d) 6.6 mA
An L-C circuit containing an 80.0-mH inductor and a 1.25-nF capacitor oscillates with a maximum current of 0.750 A. Calculate:
(a) the maximum charge on the capacitor  
(b) the oscillation frequency of the circuit
(c) Assuming the capacitor had its maximum charge at time t = 0, calculate the energy stored in the inductor after 2.50 ms of oscillation.
Answer:  (a) 7.5 µC  (b) 15.9 kHz  (c) 19.9 mJ