PHY 131 Exam #2 Calculations

A 0.30-m-long metal rod has a radius of 5.0 cm and a resistance of 2.5 × 10−5 Ω. What is the resistivity of the metal?

6.5E-7 ohm*m

A certain material is in a room at 29°C. If the absolute temperature (K) of the material is tripled, its resistance doubles. (Water freezes at 273 K.) What is the value for α, the temperature coefficient of resistivity?

0.0017 (C)^-1

. An electric car is designed to run off a bank of 13.0-V batteries with total energy storage of 3.00 × 107 J. If the electric motor draws 7 150 W, what current will be delivered to the motor?

550 A

A 1 000-V battery, a 3 000-Ω resistor, and a 0.50-μF capacitor are connected in series with a switch. The time constant for such a circuit, designated by the Greek letter, τ, is defined as the time that the capacitor takes to charge to 63% of its capacity after the switch is closed. What is the current in the circuit at a time interval of τ seconds after the switch has been closed?

0.12 A

Number 10 copper wire (radius = 1.5 mm) is commonly used for electrical installations in homes. What is the voltage drop in 15 m of #10 copper wire if it carries a current of 12 A? (The resistivity of copper is 1.7 × 10−8 Ω⋅m.)

0.43 V

A copper cable needs to carry a current of 150 A with a power loss of only 4.0 W/m. What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−8 Ω⋅m).

0.55 cm

Three resistors connected in parallel have individual values of 4.0, 6.0, and 10.0 Ω, respectively. If this combination is connected in series with a 12-V battery and a 2.0-Ω resistor, what is the current in the 10.0-Ω resistor?

0.59 A

Two singly ionized isotopes, X and Y, of the same element move with the same speed perpendicular to a uniform magnetic field. Isotope X follows a path of radius 3.24 cm while isotope Y moves along a path 3.52 cm in radius. What is the ratio of the two isotope masses, ?

0.920

What is the current through the 2.0-Ω resistor?

1.0 A

. A copper wire of length 25.0 cm is in a magnetic field of 0.38 T. If it has a mass of 11.0 g, what is the minimum current through the wire that would cause a magnetic force equal to its weight?

1.1 A

A superconducting wire carries a current of 6.0 kA. Find the magnetic field at a distance of 1.0 m from the wire. (µ0 = 4π × 10−7 T⋅m/A)

1.2E-3 T

A circular loop carrying a current of 2.4 A is oriented in a magnetic field of 0.42 T. The loop has an area of 0.33 m 2 and is mounted on an axis, perpendicular to the magnetic field, which allows the loop to rotate. What is the torque on the loop when its plane is oriented at a 25° angle to the field?

1.4E-1 N*m

What is the current through the 8.0-Ω resistor?

1.5 A

f I = 2.0 mA and the potential difference, VA - VB = +30 V in the circuit segment shown, determine the charge and polarity of the capacitor.

1.5 mC, left plate is positive

The heating coil of a hot water heater has a resistance of 19 Ω and operates at 300 V. How long a time is required to raise the temperature of 115 kg of water from 18°C to 75°C? (The specific heat for water = 103 cal/kg⋅°C and 1.0 cal = 4.186 J).

1.6 h

. Resistors of values R1 = 6.00 Ω, R2 = 4.00 Ω, R3 = 10.0 Ω, and R4 = 7.00 Ω are combined as shown. What is the equivalent resistance for this combination?

10.7 ohms

A solar panel measures 60 cm × 59 cm. In direct sunlight, the panel delivers 3.1 A at 12 V. If the intensity of sunlight is 1 000 W/m2 , what is the efficiency of the solar panel in converting solar energy into electrical energy?

11%

When a 26.0-Ω resistor is connected across a 4.50-V battery, a current of 480 mA flows. What is the resulting terminal voltage of the battery?

12.5 V

A high-voltage transmission line of diameter 2.5 cm and length 250 km carries a steady current of 1 000 A. If the conductor is copper with a free charge density of 8 × 1028 electrons/m3 , how long does it take one electron to travel the full length of the cable? (e = 1.6 × 10−19 C)

15.7E8 s

At the Fermilab accelerator in Weston, Illinois, singly-charged ions with momentum 4.0 × 10−16 kg⋅m/s are held in a circular orbit of radius 1.00 km by an upward magnetic field. What B field must be used to maintain the ions in this orbit? (qion = 1.60 × 10−19 C)

2.5 T

A 114-m-long wire carrying a current of 3.3 A will be accompanied by a magnetic field of what strength at a distance of 0.026 m from the wire? (magnetic permeability in empty space µ0 = 4π × 10−7 T⋅m/A)

2.5E-5 T

A light bulb drawing a current of 0.60 A is run for 2.0 hours. How many electrons pass through the bulb during this process?

2.7 x 10^22

Two resistors of values 7.0 and 15.0 Ω are connected in parallel. This combination in turn is hooked in series with a 3.0-Ω resistor and a 22.3-V battery. What is the current in the 3.0-Ω resistor?

2.9 A

A hair dryer draws 1 400 W, a curling iron draws 850 W, and an electric light fixture draws 600 W. If all three of these appliances are operating in parallel on a 120-V circuit, what is the total current drawn?

23.8 A

A proton is released such that it has an initial speed of 4.8 × 105 m/s from left to right across the page. A magnetic field of 1.2 T is present at an angle of 25° to the horizontal direction (or positive x axis). What is the magnitude of the force experienced by the proton? (qp = 1.6 × 10−19 C)

3.9E-14 N

The two ends of a 2.00 ohm resistor are connected to a 8.40 V battery. What is the current through the resistor?

4.20

The charge flowing through a light bulb attached to a 12.0-V battery in 10.0 s is 35.0 C. What is the total energy delivered to the filament during this process?

420 J

What is the resistance of the bulb?

5 ohms

A superconducting solenoid is to be designed to generate a magnetic field of 6.20 T. If the solenoid winding has 904 turns/m, what is the required current? (µ0 = 4π × 10−7 T⋅m/A)

5.5 E +3 A

What is the maximum number of 70-W light bulbs you can connect in parallel in a 120-V home circuit without tripping the 30-A circuit breaker?

51

Two long parallel wires 44.5 cm apart are carrying currents of 14.3 A and 23.8 A in the same direction. What is the magnitude of the magnetic field halfway between the wires?

8.54E-6 T

A proton is circling the Earth above the magnetic equator, where Earth's magnetic field is directed horizontally north and has a magnitude of 4.00 × 10-8 T. If the proton is moving at a speed of 2.8 × 107 m/s, how far above the surface of the Earth is the proton? Earth's radius is 6.38 × 106 m, a proton's mass is 1.67 × 10-27 kg, and its charge is 1.6 × 10-19 C.

9.26E+5 m

An 8.00-Ω resistor is connected to a battery with internal resistance of 0.250 Ω. If the terminal voltage across the battery is 9.00 V, what is the battery's emf?

9.28 V

A series RC circuit, which is made from a battery, a switch, a resistor, and a 3.45-μF capacitor, has a time constant of 12.0 ms. If an additional 12.0-μF is added in series to the 3.45-μF capacitor, what is the resulting time constant?

9.32 ms

How long is a wire made from 250 cm3 of copper if its resistance is 6.0 ohms? The resistivity of copper is 1.7 × 10-5 Ω·m.

9.4 m

A proton, mass 1.67 × 10−27 kg and charge +1.6 × 10−19 C, moves in a circular orbit perpendicular to a uniform magnetic field of 0.70 T. Find the time for the proton to make one complete circular orbit.

9.4 x 10^-8 s

Two long parallel wires 12.0 cm apart carry currents of 2.5 A and 2.8 A in the same direction. Is there any point between the two wires where the magnetic field is zero?

yes, 5.7 cm from the 2.5 A wire