PHYSIC 21 MATH STUDY GUIDE

A circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are parallel. A) zero B) 3.1 ̨ 10-3 Tm2 C) 5.5 ̨ 10-3 Tm2 D) 6.3 ̨ 10-3 Tm2

A

A power transmission line 50 km long has a total resistance of 0.60 W. A generator produces 100 V at 70 A. In order to reduce energy loss due to heating of the transmission line, the voltage is stepped up with a transformer with a turns ratio of 100:1. What percentage of the original energy is lost when the transformer is used? A) 0.0042% B) 0.042% C) 4.2% D) 42%

A

A resistance of 55 W, a capacitor of capacitive reactance 30 W, and an inductor of inductive reactance 30 W are connected in series to a 110-V, 60-Hz power source. What current flows in this circuit? A) 2.0 A B) less than 2.0 A C) more than 2.0 A D) none of the given answers

A

A series RLC circuit has R = 20.0 W, L = 200-mH, C = 10.0 mF. At what frequency should the circuit be driven in order to have maximum power transferred from the driving source? A) 113 Hz B) 167 Hz C) 277 Hz D) 960 Hz

A

A 10-W resistor is connected in series with a 20-mF capacitor. What is the impedance at 1000 Hz? A) 8.0 W B) 10 W C) 13 W D) 15 W W=OHMS

C

A DC motor of internal resistance 6.0 W is connected to a 24-V power supply. The operating current is 1.0 A at full speed. What is the back emf when the motor is running at full speed? A) zero B) 6.0 V C) 18 V D) 24 V

C

The flux through a coil changes from 4.0 ̨ 10-5 Wb to 5.0 ̨ 10-5 Wb in 0.10 s. What emf is induced in this coil? A) 5.0 ̨ 10-4 V B) 4.0 ̨ 10-4 V C) 1.0 ̨ 10-4 V D) none of the given answers

C

44) A 150-W lamp is placed into a 120-V AC outlet. What is the peak current? A) 0.80 A B) 0.88 A C) 1.25 A D) 1.77 A

D

5.0 A at 110 V flows in the primary of a transformer. Assuming 100% efficiency, how many amps at 24 V can flow in the secondary? A) 1.1 A B) 4.6 A C) 5.0 A D) 23 A

D

A 150-W lamp is placed into a 120-V AC outlet. What is the resistance of the lamp? A) 1.25 O B) 0.80 O C) 48 O D) 96 O

D

A 4.0-mH coil carries a current of 5.0 A. How much energy is stored in the coil's magnetic field? A) 2.0 mJ B) 10 mJ C) 20 mJ D) none of the given answers

D

A DC motor of internal resistance 6.0 W is connected to a 24-V power supply. The operating current is 1.0 A. What is the start-up current? A) 1.0 A B) 2.0 A C) 3.0 A D) 4.0 A

D

A circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are perpendicular. A) zero B) 3.1 ̨ 10-3 Tœm2 C) 5.5 ̨ 10-3 Tœm2 D) 6.3 ̨ 10-3 Tœm2

D

48) The current through a 50-W resistor is I = 0.80 sin (240 t). What is the rms current? A) 0.57 A B) 0.80 A C) 1.1 A D) 1.6 A

A

An ac series circuit has an impedance of 60 W and a resistance of 30 W. What is the power factor? A) 0.50 B) 0.71 C) 1.0 D) 1.4

A

An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If 120 V at 2.0 A is applied to the primary, what current is present in the secondary? A) 0.40 A B) 2.0 A C) 4.0 A D) 10 A

A

At what frequency does a 10-mF capacitor have a reactance of 1200 W? A) 13 Hz B) 42 Hz C) 60 Hz D) 83 Hz

A

In a transformer, how many turns are necessary in a 110-V primary if the 24-V secondary has 100 turns? A) 458 B) 240 C) 110 D) 22

A

The current through a 50-W resistor is I = 0.80 sin (240 t). At what frequency does the current vary? A) 38 Hz B) 76 Hz C) 120 Hz D) 240 Hz

A

The current through a 50-W resistor is I = 0.80 sin (240 t). How much power on average is dissipated in the resistor? A) 16 W B) 32 W C) 45 W D) 64 W

A

The primary of a transformer has 100 turns and its secondary has 200 turns. If the input current at the primary is 100 A, we can expect the output current at the secondary to be A) 50 A. B) 100 A. C) 200 A. D) none of the given answers

A

The secondary coil of a neon sign transformer provides 7500 V at 10.0 mA. The primary coil operates on 120 V. What does the primary draw? A) 0.625 A B) 0.625 mA C) 0.160 A D) 1.66 A

A

The windings of a DC motor have a resistance of 6.00 W. The motor operates on 120 V AC, and when running at full speed it generates a back emf of 105 V. What current does the motor draw when operating at full speed? A) 2.50 A B) 17.5 A C) 20.0 A D) 37.5 A

A

What inductance is necessary for 157 W of inductive reactance at 1000 Hz? A) 25.0 mH B) 157 mH C) 2.40 H D) 6.40 H

A

What inductance must be put in series with a 100-kW resistor at 1.0-MHz for a total impedance of 150 kW? A) 18 mH B) 0.15 H C) 0.17 H D) 1.5 H

A

What size capacitor must be placed in series with a 30-W resistor and a 40-mH coil if the resonant frequency of the circuit is to be 1000 Hz? A) 0.63 mF B) 0.50 mF C) 0.22 mF D) 0.17 mF

A

You are designing a generator with a maximum emf 8.0 V. If the generator coil has 200 turns and a cross-sectional area of 0.030 m2, what would be the frequency of the generator in a magnetic field of 0.030 T? A) 7.1 Hz B) 7.5 Hz C) 8.0 Hz D) 44 Hz

A

57) What is the capacitive reactance of a 4.7-mF capacitor at 10 kHz? A) 0.047 O B) 3.4 O C) 14 O D) 47 O

B

A 10-O resistor is connected to a 120-V ac power supply. What is the peak current through the resistor? A) 12 A B) 17 A C) 0.083 A D) 0.12 A

B

A 10-W resistor is connected to a 120-V ac power supply. What is the power dissipated in the resistor? A) 1.0 kW B) 1.4 kW C) 2.0 kW D) 2.9 kW

B

A 10-W resistor is in series with a 100-mF capacitor at 120 Hz. What is the phase angle? A) -82e B) -53e C) -37e D) -4.7e

B

A DC motor of internal resistance 6.0 W is connected to a 24-V power supply. The operating current is 1.0 A at full speed. What is the back emf when the motor is running at half speed? A) 6.0 V B) 9.0 V C) 18 V D) 24 V

B

A circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are at an angle of 30e. A) zero B) 3.1 ̨ 10-3 Tœm2 C) 5.5 ̨ 10-3 Tœm2 D) 6.3 ̨ 10-3 Tœm2

B

A coil of 160 turns and area 0.20 m2 is placed with its axis parallel to a magnetic field of 0.40 T. The magnetic field changes from 0.40 T in the x-direction to 0.40 T in the negative x-direction in 2.0 s. If the resistance of the coil is 16 W, at what rate is power generated in the coil? A) 5.0 W B) 10 W C) 15 W D) 20 W

B

A simple RL circuit contains a 6.0-W resistor and an 18-H inductor. What is this circuit's time constant? A) 108 s B) 3.0 s C) 0.33 s D) none of the given answers

B

If a 1000-W resistor is connected in series with a 20-mH inductor, what is the impedance at 1000 Hz? A) 0.13 kO B) 1.0 kO C) 1.1 kO D) 0.13 MO

B

If a 1000-W resistor is connected in series with a 20-mH inductor, what is the phase angle at 1000 Hz? A) 2.9 B) 7.2 C) 45 D) 90

B

The coil of a generator has 50 loops and a cross-sectional area of 0.25 m2. What is the maximum emf generated by this generator if it is spinning with an angular velocity of 4.0 rad/s in a 2.0 T magnetic field? A) 50 V B) 100 V C) 200 V D) 400 V

B

The cross-sectional area of an adjustable single loop is reduced from 1.0 m2 to 0.50 m2 in 0.10 s. What is the average emf that is induced in this coil if it is in a region where B = 2.0 T upward, and the coil's plane is perpendicular to B? A) 5 V B) 10 V C) 15 V D) 20 V

B

The output of a generator is 440 V at 20 A. It is to be transmitted on a line with resistance of 0.60 W. To what voltage must the generator output be stepped up with a transformer if the power loss in transmission is not to exceed 0.010% of the original power? A) 4.4 kV B) 7.3 kV C) 22 kV D) 45 kV

B

The primary of a transformer has 100 turns and its secondary has 200 turns. If the power input to the primary is 100 W, we can expect the power output of the secondary to be (neglecting frictional losses) A) 50 W. B) 100 W. C) 200 W. D) none of the given answers

B

What current flows in a 60-mH inductor when 120 V AC at a frequency of 20 kHz is applied to it? A) 8.0 mA B) 16 mA C) 24 mA D) 32 mA

B

What inductance is needed in series with a 4.7-mF capacitor for a resonant frequency of 10 kHz? A) 21 mH B) 54 mH C) 4.7 mH D) 5.4 mH

B

What is the current through a 0.0010-mF capacitor at 1000 Hz and 5.0 V? A) 5.4 mA B) 31 mA C) 3.1 mA D) 10 mA

B

What is the impedance of an ac series circuit with 12.0 W resistance, 15.0 W inductive reactance, and 10.0 W capacitive reactance? A) 11.6 O B) 13.0 O C) 21.9 O D) 27.7 O

B

What is the phase angle at 1500 Hz if a 100-W resistor, 20-mH coil, and 1.0-mF capacitor are connected in series? A) 0.014e B) 40e C) 45e D) 70e

B

What is the power factor for a series RLC circuit containing a 50-W resistor, a 10-mF capacitor, and a 0.45-H inductor, when connected to a 60-Hz power supply? A) zero B) 0.47 C) 0.79 D) 1.0

B

What is the resonant frequency of a 1.0-mF capacitor and a 15-mH coil in series? A) 15 kHz B) 1.3 kHz C) 0.77 kHz D) 67 Hz

B

What is the total impedance at 1500 Hz if a 100-W resistor, 20-mH coil, and 1.0-mF capacitor are connected in series? A) 0.19 kO B) 0.13 kO C) 0.11 kO D) 82 O

B

What resistance is needed in series with a 10-mF capacitor at 1.0 kHz for a total impedance of 45 W? A) 29 W B) 42 W C) 61 W D) 1.8 W W=OHMS

B

2.0 A in the 100-turn primary of a transformer causes 14 A to flow in the secondary. How many turns are in the secondary? A) 700 B) 114 C) 14 D) 4

C

A generator produces 60 A of current at 120 V. The voltage is usually stepped up to 4500 V by a transformer and transmitted through a power line of total resistance 1.0 W. Find the percentage power lost in the transmission line. A) 0.012% B) 0.024% C) 0.036% D) 0.048%

C

A horizontal metal bar that is 2.0 m long rotates at a constant angular velocity of 2.0 rad/s about a vertical axis through one of its ends while in a constant magnetic field of 5.0 ̨ 10-5 T. If the magnetic field vector points straight down, what emf is induced between the two ends of the bar? A) 5.6 ̨ 10-3 V B) 3.0 ̨ 10-3 V C) 2.0 ̨ 10-4 V D) 1.6 ̨ 10-4 V

C

A step-down transformer is needed to reduce a primary voltage of 120 V AC to 6.0V AC. What turns ratio is required? A) 10:1 B) 1:10 C) 20:1 D) 1:20

C

An AC generator consists of 100 turns of wire of area 0.090 m2 and total resistance 12 W. The loops rotate in a magnetic field of 0.50 T at a constant angular speed of 60 revolutions per second. Find the maximum induced current. A) 23 A B) 46 A C) 0.14 kA D) 0.28 kA

C

An AC generator consists of 100 turns of wire of area 0.090 m2 and total resistance 12 W. The loops rotate in a magnetic field of 0.50 T at a constant angular speed of 60 revolutions per second. Find the maximum induced emf. A) 0.27 kV B) 0.54 kV C) 1.7 kV D) 3.4 kV

C

An AC generator has 80 rectangular loops on its armature. Each loop is 12 cm long and 8 cm wide. The armature rotates at 1200 rpm about an axis parallel to the long side. If the loop rotates in a uniform magnetic field of 0.30 T, which is perpendicular to the axis of rotation, what will be the maximum output voltage of this generator? A) 20 V B) 27 V C) 29 V D) 35 V

C

An airplane with a wing span of 60 m flies horizontally at a location where the downward component of the Earth's magnetic field is 6.0 ̨ 10-5 T. Find the magnitude of the induced emf between the tips of the wings when the speed of the plane is 225 m/s. A) 0.41 V B) 0.61 V C) 0.81 V D) 1.2 V

C

An transformer consists of a 500-turn primary coil and a 2000-turn secondary coil. If the current in the secondary is 3.0 A, what is the current in the primary? A) 0.75 A B) 1.3 A C) 12 A D) 48 A

C

At what frequency will the capacitive reactance of a 0.010-mF capacitor be 100 W? A) 1.0 kHz B) 16 kHz C) 0.16 MHz D) 0.31 MHz

C

Suppose that you wish to construct a simple AC generator with an output of 12 V maximum when rotated at 60 Hz. A magnetic field of 0.050 T is available. If the area of the rotating coil is 100 cm2, how many turns are needed? A) 16 B) 32 C) 64 D) 128

C

The phase angle of an AC circuit is 63e. What is the power factor? A) 0.89 B) 0.55 C) 0.45 D) 0.11

C

The primary of a transformer has 100 turns and its secondary has 200 turns. If the input voltage to the primary is 100 V, we can expect the output voltage of the secondary to be A) 50 V. B) 100 V. C) 200 V. D) none of the given answer

C

The windings of a DC motor have a resistance of 6.00 W. The motor operates on 120 V AC, and when running at full speed it generates a back emf of 105 V. What is the starting current of the motor? A) 2.50 A B) 17.5 A C) 20.0 A D) 37.5 A

C

What capacitance is needed in series with a 3.7-mH inductor for a resonant frequency of 1000 Hz? A) 0.15 mF B) 15 mF C) 6.8 mF D) 0.015 mF

C

What capacitance is needed in series with a 30-W resistor at 1.0 kHz for a total impedance of 45 W? A) 34 mF B) 15 mF C) 4.7 mF D) 0.015 mF

C

What current flows at 5.0 V and 1500 Hz if a 100-W resistor, 20-mH coil, and 1.0-mF capacitor are connected in series? A) 0.13 A B) 45 mA C) 39 mA D) 11 mA

C

What is the inductive reactance of a 2.50-mH coil at 1000 Hz? A) 2500 O B) 796 O C) 15.7 O D) 2.50 O

C

What is the peak voltage in an AC circuit where the rms voltage is 120 V? A) 84.8 V B) 120 V C) 170 V D) none of the given answers

C

What is the power output in an ac series circuit with 12.0 W resistance, 15.0 W inductive reactance, and 10.0 W capacitive reactance, when the circuit is connected to a 120-V power supply? A) 0.60 kW B) 0.10 kW C) 0.11 kW D) 0.12 kW

C

What resistance is needed in a series circuit with a 20-mH coil and 1.0-mF capacitor for a total impedance of 100 W at 1500 Hz? A) 0.16 kW B) 82 W C) 57 W D) 18 W W=0HMS

C

What resistance must be put in series with a 450-mH inductor at 5000 Hz for a total impedance of 40000 W? A) 45 kW B) 40 kW C) 37 kW D) 26 kW W=OHMS

C

) A square coil of wire with 15 turns and an area of 0.40 m2 is placed parallel to a magnetic field of 0.75 T. The coil is flipped so its plane is perpendicular to the magnetic field in 0.050 s. What is the magnitude of the average induced emf? A) 6.0 V B) 36 V C) 45 V D) 90 V

D

100 kW is transmitted down a 6-W line at 1000 V. How much less power would be lost if the power were transmitted at 3000 V instead of at 1000 V? A) 1.0 kW B) 10 kW C) 30 kW D) 53 kW

D

A coil is wrapped with 200 turns of wire on a square frame with sides 18 cm. A uniform magnetic field is applied perpendicular to the plane of the coil. If the field changes uniformly from 0.50 T to 0 in 8.0 s, find the average value of the induced emf. A) 2.1 mV B) 4.1 mV C) 0.21 V D) 0.41 V

D

A flux of 4.0 ̨ 10-5 Wb is maintained through a coil for 0.50 s. What emf is induced in this coil by this flux? A) 8.0 ̨ 10-5 V B) 4.0 ̨ 10-5 V C) 2.0 ̨ 10-5 V D) No emf is induced in this coil.

D

A generator produces 60 A of current at 120 V. The voltage is usually stepped up to 4500 V by a transformer and transmitted through a power line of total resistance 1.0 W. Find the number of turns in the secondary if the primary has 200 turns. A) 5 B) 200 C) 4500 D) 7500

D

A generator produces 60 A of current at 120 V. The voltage is usually stepped up to 4500 V by a transformer and transmitted through a power line of total resistance 1.0 W. Find the percentage power lost in the transmission line if the voltage is not stepped up. A) 0.018% B) 0.036% C) 25% D) 50%

D

A power transmission line 50 km long has a total resistance of 0.60 W. A generator produces 100 V at 70 A. In order to reduce energy loss due to heating of the transmission line, the voltage is stepped up with a transformer with a turns ratio of 100:1. What percentage of the original energy would be lost if the transformer were not used? A) 0.0042% B) 0.042% C) 4.2% D) 42%

D

A series RLC circuit consists of a 100-W resistor, a 10.0-mF capacitor, and a 0.350-H inductor. The circuit is connected to a 120-V, 60-Hz power supply. What is the rms current in the circuit? A) 0.42 A B) 0.52 A C) 0.62 A D) 0.72 A

D

An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If 120 V at 2.0 A is applied to the primary, what voltage is present in the secondary? A) 24 V B) 120 V C) 240 V D) 600 V

D

At what frequency will a 14.0-mH coil have 14.0 W of inductive reactance? A) 1000 Hz B) 505 Hz C) 257 Hz D) 159 Hz

D

What inductance is necessary in series with a 500-W resistor for a phase angle of 40e at 10 kHz? A) 84 mH B) 46 mH C) 20 mH D) 6.7 mH

D

What is the current through a 2.50-mH coil due to a 110-V, 60.0 Hz source? A) 0.94 A B) 2.5 A C) 104 A D) 117 A

D

What is the phase angle for a series RLC circuit containing a 50-W resistor, a 10-mF capacitor, and a 0.45-H inductor, when connected to a 60-Hz power supply? A) 38e B) -38e C) 62e D) -62e

D

What resistance is needed in series with a 10-mF capacitor at 1.0 kHz for a phase angle of 40e? A) 0.40 W B) 2.5 W C) 16 W D) 19 W

D

What size capacitor is needed to have 50 W of capacitive reactance at 10 kHz? A) 16 mF B) 5.0 mF C) 3.2 mF D) 0.32 mF

D

Which of the following capacitances is needed in series with a 100-W resistor and 15-mH coil to get a total impedance of 110 W at 2000 Hz? A) 0.14 mF B) 46 mF C) 10 mF D) 0.56 mF

D