13.6 Electric generators and back emf  (Page 4/7)

Design a current loop that, when rotated in a uniform magnetic field of strength 0.10 T, will produce an emf $\epsilon ={\epsilon }_0\text{sin}\omega t,$ where ${\epsilon }_0=110\text{V}$ and $\omega =120\pi \text{rad/s}\text{.}$

A flat, square coil of 20 turns that has sides of length 15.0 cm is rotating in a magnetic field of strength 0.050 T. If the maximum emf produced in the coil is 30.0 mV, what is the angular velocity of the coil?

A 50-turn rectangular coil with dimensions $0.15\text{m}\times 0.40\text{m}$ rotates in a uniform magnetic field of magnitude 0.75 T at 3600 rev/min. (a) Determine the emf induced in the coil as a function of time. (b) If the coil is connected to a $1000\text{-}\text{Ω}$ resistor, what is the power as a function of time required to keep the coil turning at 3600 rpm? (c) Answer part (b) if the coil is connected to a 2000- $\text{Ω}$ resistor.

The square armature coil of an alternating current generator has 200 turns and is 20.0 cm on side. When it rotates at 3600 rpm, its peak output voltage is 120 V. (a) What is the frequency of the output voltage? (b) What is the strength of the magnetic field in which the coil is turning?

A flip coil is a relatively simple device used to measure a magnetic field. It consists of a circular coil of N turns wound with fine conducting wire. The coil is attached to a ballistic galvanometer, a device that measures the total charge that passes through it. The coil is placed in a magnetic field $\overrightarrow{B}$ such that its face is perpendicular to the field. It is then flipped through $180\text{°},$ and the total charge Q that flows through the galvanometer is measured. (a) If the total resistance of the coil and galvanometer is R , what is the relationship between B and Q ? Because the coil is very small, you can assume that $\overrightarrow{B}$ is uniform over it. (b) How can you determine whether or not the magnetic field is perpendicular to the face of the coil?

The flip coil of the preceding problem has a radius of 3.0 cm and is wound with 40 turns of copper wire. The total resistance of the coil and ballistic galvanometer is $0.20\text{Ω.}$ When the coil is flipped through $180\text{°}$ in a magnetic field $\overrightarrow{B},$ a change of 0.090 C flows through the ballistic galvanometer. (a) Assuming that $\overrightarrow{B}$ and the face of the coil are initially perpendicular, what is the magnetic field? (b) If the coil is flipped through $90\text{°},$ what is the reading of the galvanometer?

A 120-V, series-wound motor has a field resistance of 80 $\text{Ω}$ and an armature resistance of 10 $\text{Ω}$ . When it is operating at full speed, a back emf of 75 V is generated. (a) What is the initial current drawn by the motor? When the motor is operating at full speed, where are (b) the current drawn by the motor, (c) the power output of the source, (d) the power output of the motor, and (e) the power dissipated in the two resistances?

A small series-wound dc motor is operated from a 12-V car battery. Under a normal load, the motor draws 4.0 A, and when the armature is clamped so that it cannot turn, the motor draws 24 A. What is the back emf when the motor is operating normally?